title:
Combined effects of compressibility and helicity on the scaling regimes
  of a passive scalar advected by turbulent velocity field with finite
  correlation time

abstract:
  The influence of compressibility and helicity on the stability of the scaling
regimes of a passive scalar advected by a Gaussian velocity field with finite
correlation time is investigated by the field theoretic renormalization group
within two-loop approximation. The influence of helicity and compressibility on
the scaling regimes is discussed as a function of the exponents $\epsilon$ and
$\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity
field in the inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related
to the correlation time at the wave number $k$ which is scaled as
$k^{-2+\eta}$. The restrictions given by nonzero compressibility and helicity
on the regions with stable infrared fixed points which correspond to the stable
infrared scaling regimes are discussed. A special attention is paid to the case
of so-called frozen velocity field when the velocity correlator is time
independent. In this case, explicit inequalities which must be fulfilled in the
plane $\epsilon-\eta$ are determined within two-loop approximation.


title:
Synchronization of extended chaotic systems with long-range
  interactions: an analogy to Levy-flight spreading of epidemics

abstract:
  Spatially extended chaotic systems with power-law decaying interactions are
considered. Two coupled replicas of such systems synchronize to a common
spatio-temporal chaotic state above a certain coupling strength. The
synchronization transition is studied as a nonequilibrium phase transition and
its critical properties are analyzed at varying the interaction range. The
transition is found to be always continuous, while the critical indexes vary
with continuity with the power law exponent characterizing the interaction.
Strong numerical evidences indicate that the transition belongs to the {\it
anomalous directed percolation} family of universality classes found for
L{\'e}vy-flight spreading of epidemic processes.


title: Modulational instability in a layered Kerr medium: Theory and Experiment

abstract:
  We present the first experimental investigation of modulational instability
in a layered Kerr medium. The particularly interesting and appealing feature of
our configuration, consisting of alternating glass-air layers, is the
piecewise-constant nature of the material properties, which allows a
theoretical linear stability analysis leading to a Kronig-Penney equation whose
forbidden bands correspond to the modulationally unstable regimes. We find very
good {\it quantitative} agreement between theoretical, numerical, and
experimental diagnostics of the modulational instability. Because of the
periodicity in the evolution variable arising from the layered medium, there
are multiple instability regions rather than just one as in the uniform medium.


title: Semiclassical Theory for Parametric Correlation of Energy Levels

abstract:
  Parametric energy-level correlation describes the response of the
energy-level statistics to an external parameter such as the magnetic field.
Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the
parametric energy-level correlation depending on the magnetic field difference.
The small-time expansion of the spectral form factor $K(\tau)$ is shown to be
in agreement with the prediction of parameter dependent random-matrix theory to
all orders in $\tau$.


title: On recursion operators for elliptic models

abstract:
  New quasilocal recursion and Hamiltonian operators for the Krichever-Novikov
and the Landau-Lifshitz equations are found. It is shown that the associative
algebra of quasilocal recursion operators for these models is generated by a
couple of operators related by an elliptic curve equation. A theoretical
explanation of this fact for the Landau-Lifshitz equation is given in terms of
multiplicators of the corresponding Lax structure.


title: Two-dimensional dark soliton in the nonlinear Schroedinger equation

abstract:
  Two-dimensional gray solitons to the nonlinear Schroedinger equation are
numerically created by two processes to show its robustness. One is transverse
instability of a one-dimensional gray soliton, and another is a pair
annihilation of a vortex and an antivortex. The two-dimensional dark solitons
are anisotropic and propagate in a certain direction. The two-dimensional dark
soliton is stable against the head-on collision. The effective mass of the
two-dimensional dark soliton is evaluated from the motion in a harmonic
potential.


title:
Control of the chaotic velocity dispersion of a cold electron beam
  interacting with electrostatic waves

abstract:
  In this article we present an application of a method of control of
Hamiltonian systems to the chaotic velocity diffusion of a cold electron beam
interacting with electrostatic waves. We numerically show the efficiency and
robustness of the additional small control term in restoring kinetic coherence
of the injected electron beam.


title:
Bifurcation and Chaos in Coupled Periodically Forced Non-identical
  Duffing Oscillators

abstract:
  We study the bifurcations and the chaotic behaviour of a periodically forced
double-well Duffing oscillator coupled to a single-well Duffing oscillator.
Using the amplitude and the frequency of the driving force as control
parameters, we show that our model presents phenomena which were not observed
in coupled periodically forced Duffing oscillators with identical potentials.
In the regime of relatively weak coupling, bubbles of bifurcations and chains
of symmetry-breaking are identified. For much stronger couplings, Hopf
bifurcations born from orbits of higher periodicity and supercritical Neimark
bifurcations emerge. Moreover, tori-breakdown route to a strange non-chaotic
attractor is also another highlight of features found in this model.


title: Transport in Thin Gravity-driven Flow over a Curved Substrate

abstract:
  We consider steady gravity-driven flow of a thin layer of viscous fluid over
a curved substrate. The substrate has topographical variations (`bumps') on a
large scale compared to the layer thickness. Using lubrication theory, we find
the velocity field in generalized curvilinear coordinates. We correct the
velocity field so as to satisfy kinematic constraints, which is essential to
avoid particles escaping the fluid when computing their trajectories. We then
investigate the particle transport properties of flows over substrates with
translational symmetry, where chaotic motion is precluded. The existence of
trapped and untrapped trajectories leads to complicated transport properties
even for this simple case. For more general substrate shapes, the trajectories
chaotically jump between trapped and untrapped motions.


title:
The effect of symmetry breaking on the dynamics near a structurally
  stable heteroclinic cycle between equilibria and a periodic orbit

abstract:
  The effect of small forced symmetry breaking on the dynamics near a
structurally stable heteroclinic cycle connecting two equilibria and a periodic
orbit is investigated. This type of system is known to exhibit complicated,
possibly chaotic dynamics including irregular switching of sign of various
phase space variables, but details of the mechanisms underlying the complicated
dynamics have not previously been investigated. We identify global bifurcations
that induce the onset of chaotic dynamics and switching near a heteroclinic
cycle of this type, and by construction and analysis of approximate return
maps, locate the global bifurcations in parameter space. We find there is a
threshold in the size of certain symmetry-breaking terms below which there can
be no persistent switching. Our results are illustrated by a numerical example.


title: Symbolic Dynamics in a Matching Labour Market Model

abstract:
  In this paper we apply the techniques of symbolic dynamics to the analysis of
a labor market which shows large volatility in employment flows. In a recent
paper, Bhattacharya and Bunzel \cite{BB} have found that the discrete time
version of the Pissarides-Mortensen matching model can easily lead to chaotic
dynamics under standard sets of parameter values. To conclude about the
existence of chaotic dynamics in the numerical examples presented in the paper,
the Li-Yorke theorem or the Mitra sufficient condition were applied which seems
questionable because they may lead to misleading conclusions. Moreover, in a
more recent version of the paper, Bhattacharya and Bunzel \cite{BB1} present
new results in which chaos is completely removed from the dynamics of the
model. Our paper explores the matching model so interestingly developed by the
authors with the following objectives in mind: (i) to show that chaotic
dynamics may still be present in the model for standard parameter values; (ii)
to clarify some open questions raised by the authors in \cite{BB}, by providing
a rigorous proof of the existence of chaotic dynamics in the model through the
computation of topological entropy in a symbolic dynamics setting.


title:
Chaos, Fractal and Quantum Poincare Recurrences in Diamagnetic Kepler
  Problem

abstract:
  The statistics of quantum Poincare recurrences in Hilbert space for
diamagnetic hydrogen atom in strong magnetic field has been investigated. It
has been shown that quantities characterizing classical chaos are in a good
agreement with the ones that are used to describe quantum chaos. The equality
of classical and quantum Poincare recurrences has been shown. It has been
proved that one of the signs of the emergence of quantum chaos is the
irreversible transition from a pure quantum mechanical state to the mixed one.


title: Energy evolution in time-dependent harmonic oscillator

abstract:
  The theory of adiabatic invariants has a long history, and very important
implications and applications in many different branches of physics,
classically and quantally, but is rarely founded on rigorous results. Here we
treat the general time-dependent one-dimensional harmonic oscillator, whose
Newton equation $\ddot{q} + \omega^2(t) q=0$ cannot be solved in general. We
follow the time-evolution of an initial ensemble of phase points with sharply
defined energy $E_0$ at time $t=0$ and calculate rigorously the distribution of
energy $E_1$ after time $t=T$, which is fully (all moments, including the
variance $\mu^2$) determined by the first moment $\bar{E_1}$. For example,
$\mu^2 = E_0^2 [(\bar{E_1}/E_0)^2 - (\omega (T)/\omega (0))^2]/2$, and all
higher even moments are powers of $\mu^2$, whilst the odd ones vanish
identically. This distribution function does not depend on any further details
of the function $\omega (t)$ and is in this sense universal. In ideal
adiabaticity $\bar{E_1} = \omega(T) E_0/\omega(0)$, and the variance $\mu^2$ is
zero, whilst for finite $T$ we calculate $\bar{E_1}$, and $\mu^2$ for the
general case using exact WKB-theory to all orders. We prove that if $\omega
(t)$ is of class ${\cal C}^{m}$ (all derivatives up to and including the order
$m$ are continuous) $\mu \propto T^{-(m+1)}$, whilst for class ${\cal
C}^{\infty}$ it is known to be exponential $\mu \propto \exp (-\alpha T)$.


title:
The Lyapunov stability of the N-soliton solutions in the Lax hierarchy
  of the Benjamin-Ono equation

abstract:
  The Lyapunov stability is established for the N-soliton solutions in the Lax
hierarchy of the Benjamin-Ono (BO) equation. We characterize the N-soliton
profiles as critical points of certain Lyapunov functional. By using several
results derived by the inverse scattering transform of the BO equation, we
demonstarate the convexity of the Lyapunov functional when evaluated at the
N-soliton profiles. From this fact, we deduce that the N-soliton solutions are
energetically stable.


title:
Thermal diffusion of solitons on anharmonic chains with long-range
  coupling

abstract:
  We extend our studies of thermal diffusion of non-topological solitons to
anharmonic FPU-type chains with additional long-range couplings. The observed
superdiffusive behavior in the case of nearest neighbor interaction (NNI) turns
out to be the dominating mechanism for the soliton diffusion on chains with
long-range interactions (LRI). Using a collective variable technique in the
framework of a variational analysis for the continuum approximation of the
chain, we derive a set of stochastic integro-differential equations for the
collective variables (CV) soliton position and the inverse soliton width. This
set can be reduced to a statistically equivalent set of Langevin-type equations
for the CV, which shares the same Fokker-Planck equation. The solution of the
Langevin set and the Langevin dynamics simulations of the discrete system agree
well and demonstrate that the variance of the soliton increases stronger than
linearly with time (superdiffusion). This result for the soliton diffusion on
anharmonic chains with long-range interactions reinforces the conjecture that
superdiffusion is a generic feature of non-topological solitons.


title:
On application of Liouville type equations to constructing B\"acklund
  transformations

abstract:
  It is shown how pseudoconstants of the Liouville-type equations can be
exploited as a tool for construction of the B\"acklund transformations. Several
new examples of such transformations are found. In particular we obtained the
B\"acklund transformations for a pair of three-component analogs of the
dispersive water wave system, and auto-B\"acklund transformations for coupled
three-component KdV-type systems.


title: Semiclassical universality of parametric spectral correlations

abstract:
  We consider quantum systems with a chaotic classical limit that depend on an
external parameter, and study correlations between the spectra at different
parameter values. In particular, we consider the parametric spectral form
factor $K(\tau,x)$ which depends on a scaled parameter difference $x$. For
parameter variations that do not change the symmetry of the system we show by
using semiclassical periodic orbit expansions that the small $\tau$ expansion
of the form factor agrees with Random Matrix Theory for systems with and
without time reversal symmetry.


title:
Lagrangian analysis of alignment dynamics for isentropic compressible
  magnetohydrodynamics

abstract:
  After a review of the isentropic compressible magnetohydrodynamics (ICMHD)
equations, a quaternionic framework for studying the alignment dynamics of a
general fluid flow is explained and applied to the ICMHD equations.


title:
Dispersionless integrable equations as coisotropic deformations.
  Extensions and reductions

abstract:
  Interpretation of dispersionless integrable hierarchies as equations of
coisotropic deformations for certain algebras and other algebraic structures
like Jordan triple systInterpretation of dispersionless integrable hierarchies
as equations of coisotropic deformations for certain algebras and other
algebraic structures like Jordan triple systems is discussed. Several
generalizations are considered. Stationary reductions of the dispersionless
integrable equations are shown to be connected with the dynamical systems on
the plane completely integrable on a fixed energy level. ems is discussed.
Several generalizations are considered. Stationary reductions of the
dispersionless integrable equations are shown to be connected with the
dynamical systems on the plane completely integrable on a fixed energy level.


title: Geometric order parameter equations

abstract:
  Aggregation of particles whose interaction potential depends on their mutual
orientation is considered. The aggregation dynamics is derived using a version
of Darcy's law and a variational principle depending on the geometric nature of
the physical quantities. The evolution equations that result separate into two
classes: either characteristic equations, or gradient flow equations. We derive
analytical solutions of both types of equations which are collapsed (clumped)
states and show their dynamical emergence from smooth initial conditions in
numerical simuations.


title: Instability and Evolution of Nonlinearly Interacting Water Waves

abstract:
  We consider the modulational instability of nonlinearly interacting
two-dimensional waves in deep water, which are described by a pair of
two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear
dispersion relation. The latter is numerically analyzed to obtain the regions
and the associated growth rates of the modulational instability. Furthermore,
we follow the long term evolution of the latter by means of computer
simulations of the governing nonlinear equations and demonstrate the formation
of localized coherent wave envelopes. Our results should be useful for
understanding the formation and nonlinear propagation characteristics of large
amplitude freak waves in deep water.


title:
Computing fractal dimension in supertransient systems directly, fast and
  reliable

abstract:
  Chaotic transients occur in many experiments including those in fluids, in
simulations of the plane Couette flow, and in coupled map lattices and they are
a common phenomena in dynamical systems. Superlong chaotic transients are
caused by the presence of chaotic saddles whose stable sets have fractal
dimensions that are close to phase-space dimension. For many physical systems
chaotic saddles have a big impact on laboratory measurements, and it is
important to compute the dimension of such stable sets including fractal basin
boundaries through a direct method. In this work, we present a new method to
compute the dimension of stable sets of chaotic saddles directly, fast, and
reliable.


title:
Ambiguity in the Determination of the Free Energy for a Model of the
  Circle Map

abstract:
  We consider a simple model to describe the widths of the mode locked
intervals for the critical circle map. Using two different partitions of the
rational numbers, based on Farey series and Farey tree levels respectively, we
calculate the free energy analytically at selected points for each partition.
It is found that the result of the calculation depends on the method of
partition. An implication of this is that the generalized dimensions $D_q$ are
different for each partition except when $q=0$, i.e. only the Hausdorff
dimension is the same in each case.


title: Delayed-mutual coupling dynamics of lasers: scaling laws and resonances

abstract:
  We consider a model for two lasers that are mutually coupled
optoelectronically by modulating the pump of one laser with the intensity
deviations of the other. Signal propagation time in the optoelectronic loop
causes a significant delay leading to the onset of oscillatory output.
Multiscale perturbation methods are used to describe the amplitude and period
of oscillations as a function of the coupling strength and delay time. For weak
coupling the oscillations have the laser's relaxation period, and the amplitude
varies as the one-fourth power of the parameter deviations from the bifurcation
point. For order-one coupling strength the period is determined as multiples of
the delay time, and the amplitude varies with a square-root power law. Because
we allow for independent control of the individual coupling constants, for
certain parameter values there is an atypical amplitude-resonance phenomena.
Finally, our theoretical results are consistent with recent experimental
observations when the inclusion of a low-pass filter in the coupling loop is
taken into account.


title: Statistical properties of the continuum Salerno model

abstract:
  The statistical properties of the Salerno model is investigated.
  In particular, a comparison between the coherent and partially coherent wave
modes is made for the case of a random phased wave packet. It is found that the
random phased induced spectral broadening gives rise to damping of
instabilities, but also a broadening of the instability region in
quasi-particle momentum space. The results can be of significance for
condensation of magnetic moment bosons in deep optical lattices.


title: From nonassociativity to solutions of the KP hierarchy

abstract:
  A recently observed relation between 'weakly nonassociative' algebras A (for
which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent
variable in the middle nucleus A' of A) is recalled. For any such algebra there
is a nonassociative hierarchy of ODEs, the solutions of which determine
solutions of the KP hierarchy. In a special case, and with A' a matrix algebra,
this becomes a matrix Riccati hierarchy which is easily solved. The matrix
solution then leads to solutions of the scalar KP hierarchy. We discuss some
classes of solutions obtained in this way.


title: Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

abstract:
  This paper is mainly a review of the multi--Hamiltonian nature of Toda and
generalized Toda lattices corresponding to the classical simple Lie groups but
it includes also some new results. The areas investigated include master
symmetries, recursion operators, higher Poisson brackets, invariants and group
symmetries for the systems. In addition to the positive hierarchy we also
consider the negative hierarchy which is crucial in establishing the
bi--Hamiltonian structure for each particular simple Lie group. Finally, we
include some results on point and Noether symmetries and an interesting
connection with the exponents of simple Lie groups. The case of exceptional
simple Lie groups is still an open problem.


title:
Bifurcations and sudden current change in ensembles of classically
  chaotic ratchets

abstract:
  In \prl 84, 258 (2000), Mateos conjectured that current reversal in a
classical deterministic ratchet is associated with bifurcations from chaotic to
periodic regimes. This is based on the comparison of the current and the
bifurcation diagram as a function of a given parameter for a periodic
asymmetric potential. Barbi and Salerno, in \pre 62, 1988 (2000), have further
investigated this claim and argue that, contrary to Mateos' claim, current
reversals can occur also in the absence of bifurcations. Barbi and Salerno's
studies are based on the dynamics of one particle rather than the statistical
mechanics of an ensemble of particles moving in the chaotic system. The
behavior of ensembles can be quite different, depending upon their
characteristics, which leaves their results open to question. In this paper we
present results from studies showing how the current depends on the details of
the ensemble used to generate it, as well as conditions for convergent behavior
(that is, independent of the details of the ensemble). We are then able to
present the converged current as a function of parameters, in the same system
as Mateos as well as Barbi and Salerno. We show evidence for current reversal
without bifurcation, as well as bifurcation without current reversal. We
conjecture that it is appropriate to correlate abrupt changes in the current
with bifurcation, rather than current reversals, and show numerical evidence
for our claims.


title:
Cryptanalysis of a chaotic block cipher with external key and its
  improved version

abstract:
  Recently, Pareek et al. proposed a symmetric key block cipher using multiple
one-dimensional chaotic maps. This paper reports some new findings on the
security problems of this kind of chaotic cipher: 1) a number of weak keys
exists; 2) some important intermediate data of the cipher are not sufficiently
random; 3) the whole secret key can be broken by a known-plaintext attack with
only 120 consecutive known plain-bytes in one known plaintext. In addition, it
is pointed out that an improved version of the chaotic cipher proposed by Wei
et al. still suffers from all the same security defects.


title: Reliable and unreliable dynamics in driven coupled oscillators

abstract:
  This letter concerns the reliability of coupled oscillator networks in
response to fluctuating inputs. Reliability means that (following a transient)
an input elicits identical responses upon repeated presentations, regardless of
the system's initial condition. Here, we analyze this property for two coupled
oscillators, demonstrating that oscillator networks exhibit both reliable and
unreliable dynamics for broad ranges of coupling strengths. We further argue
that unreliable dynamics are characterized by strange attractors with random
SRB measures, implying that though unreliable, the responses lie on
low-dimensional sets. Finally, we show that 1:1 phase locking in the zero-input
system corresponds to high susceptibility for unreliable responses. A geometric
explanation is proposed.


title: Fluctuations and Transients in Quantum-Resonant Evolution

abstract:
  The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked
particle is studied in detail on different time scales for {\em general}
kicking potentials. It is shown that the asymptotic time behavior of a
wave-packet MKE is typically a linear growth with bounded fluctuations having a
simple number-theoretical origin. For a large class of wave packets, the MKE is
shown to be exactly the superposition of its asymptotic behavior and transient
logarithmic corrections. Both fluctuations and transients can be significant
for not too large times but they may vanish identically under some conditions.
In the case of incoherent mixtures of plane waves, it is shown that the MKE
never exhibits asymptotic fluctuations but transients usually occur.

categories: nlin.CD cond-mat.mes-hall physics.atom-ph quant-ph


title:
Dark Solitons in Discrete Lattices: Saturable versus Cubic
  Nonlinearities

abstract:
  In the present work, we study dark solitons in dynamical lattices with the
saturable nonlinearity and compare them with those in lattices with the cubic
nonlinearity. This comparison has become especially relevant in light of recent
experimental developments in the former context. The stability properties of
the fundamental waves, for both on-site and inter-site modes, are examined
analytically and corroborated by numerical results. Furthermore, their
dynamical evolution when they are found to be unstable is obtained through
appropriately crafted numerical experiments.


title: Long-range effects on superdiffusive solitons in anharmonic chains

abstract:
  Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam
(FPU)-like lattices were recently generalized to the case of dispersive
long-range interactions (LRI) of the Kac-Baker form. The position variance of
the soliton shows a stronger than linear time-dependence (superdiffusion) as
found earlier for lattice solitons on FPU chains with nearest neighbour
interactions (NNI). In contrast to the NNI case where the position variance at
moderate soliton velocities has a considerable linear time-dependence (normal
diffusion), the solitons with LRI are dominated by a superdiffusive mechanism
where the position variance mainly depends quadratic and cubic on time. Since
the superdiffusion seems to be generic for nontopological solitons, we want to
illuminate the role of the soliton shape on the superdiffusive mechanism.
Therefore, we concentrate on a FPU-like lattice with a certain class of
power-law long-range interactions where the solitons have algebraic tails
instead of exponential tails in the case of FPU-type interactions (with or
without Kac-Baker LRI). A collective variable (CV) approach in the continuum
approximation of the system leads to stochastic integro-differential equations
which can be reduced to Langevin-type equations for the CV position and width.
We are able to derive an analytical result for the soliton diffusion which
agrees well with the simulations of the discrete system. Despite of
structurally similar Langevin systems for the two soliton types, the algebraic
solitons reach the superdiffusive long-time limit with a characteristic
$t^{1.5}$ time-dependence much faster than exponential solitons. The soliton
shape determines the diffusion constant in the long-time limit that is
approximately a factor of $\pi$ smaller for algebraic solitons.


title: Exact energy distribution function in time-dependent harmonic oscillator

abstract:
  Following a recent work by Robnik and Romanovski (J.Phys.A: Math.Gen. {\bf
39} (2006) L35, Open Syst. & Infor. Dyn. {\bf 13} (2006) 197-222) we derive the
explicit formula for the universal distribution function of the final energies
in a time-dependent 1D harmonic oscillator, whose functional form does not
depend on the details of the frequency $\omega (t)$, and is closely related to
the conservation of the adiabatic invariant. The normalized distribution
function is $P(x) = \pi^{-1} (2\mu^2 - x^2)^{-{1/2}}$, where $x=E_1-
\bar{E_1}$, $E_1$ is the final energy, $\bar{E_1}$ is its average value, and
$\mu^2$ is the variance of $E_1$. $\bar{E_1}$ and $\mu^2$ can be calculated
exactly using the WKB approach to all orders.


title:
On determination of statistical properties of spectra from parametric
  level dynamics

abstract:
  We analyze an approach aiming at determining statistical properties of
spectra of time-periodic quantum chaotic system based on the parameter dynamics
of their quasienergies. In particular we show that application of the methods
of statistical physics, proposed previously in the literature, taking into
account appropriate integrals of motion of the parametric dynamics is fully
justified, even if the used integrals of motion do not determine the invariant
manifold in a unique way. The indetermination of the manifold is removed by
applying Dirac's theory of constrained Hamiltonian systems and imposing
appropriate primary, first-class constraints and a gauge transformation
generated by them in the standard way. The obtained results close the gap in
the whole reasoning aiming at understanding statistical properties of spectra
in terms of parametric dynamics.


title: Non-Reversible Evolution of Quantum Chaotic System. Kinetic Description

abstract:
  Time dependent dynamics of the chaotic quantum-mechanical system has been
studied. Irreversibility of the dynamics is shown. It is shown, that being in
the initial moment in pure quantum-mechanical state, system makes irreversible
transition into mixed state. Original mechanism of mixed state formation is
offered. Quantum kinetic equation is obtained. Growth of the entropy during the
evolution process is estimated.


title: Universality in Complex Networks: Random Matrix Analysis

abstract:
  We apply random matrix theory to complex networks. We show that nearest
neighbor spacing distribution of the eigenvalues of the adjacency matrices of
various model networks, namely scale-free, small-world and random networks
follow universal Gaussian orthogonal ensemble statistics of random matrix
theory. Secondly we show an analogy between the onset of small-world behavior,
quantified by the structural properties of networks, and the transition from
Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody
parameter characterizing a spectral property. We also present our analysis for
a protein-protein interaction network in budding yeast.

categories: nlin.AO cond-mat.dis-nn cond-mat.other cond-mat.stat-mech physics.comp-ph q-bio.MN q-bio.OT


title:
New Hamiltonian formalism and Lagrangian representations for integrable
  hydrodynamic type systems

abstract:
  New Hamiltonian formalism based on the theory of conjugate curvilinear
coordinate nets is established. All formulas are ``mirrored'' to corresponding
formulas in the Hamiltonian formalism constructed by B.A. Dubrovin and S.P.
Novikov (in a flat case) and E.V. Ferapontov (in a non-flat case). In the
``mirrored-flat'' case the Lagrangian formulation is found. Multi-Hamiltonian
examples are presented. In particular Egorov's case, generalizations of local
Nutku--Olver's Hamiltonian structure and corresponding Sheftel--Teshukov's
recursion operator are presented. An number of Hamiltonian structures of all
odd orders is found.


title: On exclusion type inhomogeneous interacting particle systems

abstract:
  For a large class of inhomogeneous interacting particle systems (IPS) on a
lattice we develop a rigorous method for mapping them onto homogeneous IPS. Our
novel approach provides a direct way of obtaining the statistical properties of
such inhomogeneous systems by studying the far simpler homogeneous systems. In
the cases when the latter can be solved exactly our method yields an exact
solution for the statistical properties of an inhomogeneous IPS. This approach
is illustrated by studies of three of IPS, namely those with particles of
different sizes, or with varying (between particles) maximal velocities, or
accelerations.


title:
Nodal domains on isospectral quantum graphs: the resolution of
  isospectrality ?

abstract:
  We present and discuss isospectral quantum graphs which are not isometric.
These graphs are the analogues of the isospectral domains in R2 which were
introduced recently and are all based on Sunada's construction of isospectral
domains. After presenting some of the properties of these graphs, we discuss a
few examples which support the conjecture that by counting the nodal domains of
the corresponding eigenfunctions one can resolve the isospectral ambiguity.


title: On the problem of catastrophic relaxation in superfluid 3-He-B

abstract:
  In this Letter we discussed the parametric instability of texture of
homogeneous (in time) spin precession, explaining how spatial inhomogeneity of
the texture may change the threshold of the instability in comparison with
idealized spatial homogeneous case, considered in our JETP Letter \textbf{83},
530 (2006), cond-mat/0605386. This discussion is inspired by critical Comment
of I.A. Fomin (cond-mat/0606760) related to the above questions. In addition we
considered here results of direct numerical simulations of the full
Leggett-Takagi equation of motion for magnetization in superfluid 3He-B and
experimental data for magnetic field dependence of the catastrophic relaxation,
that provide solid support of the theory of this phenomenon, presented in our
2006 JETP Letter.


title: Polarized solitons in a cubic-quintic medium

abstract:
  The interaction of both scalar and counter-rotating polarized steady state
pulses (SSP) is studied numerically for a medium characterized by nonlinear
susceptibilities of the third and the fifth order (a cubic-quintic medium
with,$\chi_{3}>0,\chi_{5}<0$). The collision of two plateau-shaped solitons
proved to be essentially inelastic, as a number of secondary elliptically
polarized solitary waves arise as a result of interaction of steady-state
pulses.


title: Persistent localized states for a chaotically mixed bistable reaction

abstract:
  We describe the evolution of a bistable chemical reaction in a closed
two-dimensional chaotic laminar flow, from a localized initial disturbance.
When the fluid mixing is sufficiently slow, the disturbance may spread and
eventually occupy the entire fluid domain. By contrast, rapid mixing tends to
dilute the initial state and so extinguish the disturbance. Such a dichotomy is
well known. However, we report here a hitherto apparently unremarked
intermediate case, a persistent highly localized disturbance. Such a localized
state arises when the Damkoehler number is great enough to sustain a hotspot,
but not so great as to lead to global spread. We show that such a disturbance
is located in the neighborhood of an unstable periodic orbit of the flow, and
we describe some limited aspects of its behavior using a reduced, lamellar
model.


title: Synchronization in Gradient Networks

abstract:
  The contradiction between the fact that many empirical networks possess
power-law degree distribution and the finding that network of heterogeneous
degree distribution is difficult to synchronize has been a paradox in the study
of network synchronization. Surprisingly, we find that this paradox can be well
fixed when proper gradients are introduced to the network links, i.e.
heterogeneity is in favor of synchronization in gradient networks. We analyze
the statistical properties of gradient networks and explore their dependence to
the other network parameters. Based on these understandings, we further propose
a new scheme for network synchronization distinguished by using less network
information while reaching stronger synchronizability, as supported by
analytical estimates of eigenvalues and directed simulations of coupled chaotic
oscillators. Our findings suggest that, with gradient, scale-free network is a
natural choice for synchronization.


title:
Local Conservation Laws and the Hamiltonian Formalism for the Toda
  Hierarchy Revisited

abstract:
  We revisit an elementary recursive approach to local conservation laws and
the Hamiltonian formalism for the Toda hierarchy.


title: On the initial value problem of a periodic box-ball system

abstract:
  We show that the initial value problem of a periodic box-ball system can be
solved in an elementary way using simple combinatorial methods.


title:
On the Linearization of Second-Order Differential and Difference
  Equations

abstract:
  This article complements recent results of the papers [J. Math. Phys. 41
(2000), 480; 45 (2004), 336] on the symmetry classification of second-order
ordinary difference equations and meshes, as well as the Lagrangian formalism
and Noether-type integration technique. It turned out that there exist
nonlinear superposition principles for solutions of special second-order
ordinary difference equations which possess Lie group symmetries. This
superposition springs from the linearization of second-order ordinary
difference equations by means of non-point transformations which act
simultaneously on equations and meshes. These transformations become some sort
of contact transformations in the continuous limit.


title: Coupled Modified KP Hierarchy and Its Dispersionless Limit

abstract:
  We define the coupled modified KP hierarchy and its dispersionless limit.
This integrable hierarchy is a generalization of the ''half'' of the Toda
lattice hierarchy as well as an extension of the mKP hierarchy. The solutions
are parametrized by a fibered flag manifold. The dispersionless counterpart
interpolates several versions of dispersionless mKP hierarchy.


title:
Short wave length approximation of a boundary integral operator for
  homogeneous and isotropic elastic bodies

abstract:
  We derive a short wave length approximation of a boundary integral operator
for two-dimensional isotropic and homogeneous elastic bodies of arbitrary
shape. Trace formulae for elastodynamics can be deduced in this way from first
principles starting directly from Navier-Cauchy's equation.


title:
On pattern structures of the N-soliton solution of the discrete KP
  equation over a finite field

abstract:
  The existence and properties of coherent pattern in the multisoliton
solutions of the dKP equation over a finite field is investigated. To that end,
starting with an algebro-geometric construction over a finite field, we derive
a "travelling wave" formula for $N$-soliton solutions in a finite field.
However, despite it having a form similar to its analogue in the complex field
case, the finite field solutions produce patterns essentially different from
those of classical interacting solitons.


title: Violations of local equilibrium and stochastic thermostats

abstract:
  We quantitatively investigate the violations of local equilibrium in the
$\phi^4$ theory under thermal gradients, using stochastic thermostats. We find
that the deviations from local equilibrium can be quite well described by a
behavior $\sim(\nabla T)^2$. The dependence of the quantities on the thermostat
type is analyzed and its physical implications are discussed.


title:
Artificial Neural Network to predict mean monthly total ozone in Arosa,
  Switzerland

abstract:
  Present study deals with the mean monthly total ozone time series over Arosa,
Switzerland. The study period is 1932-1971. First of all, the total ozone time
series has been identified as a complex system and then Artificial Neural
Networks models in the form of Multilayer Perceptron with back propagation
learning have been developed. The models are Single-hidden-layer and
Two-hidden-layer Perceptrons with sigmoid activation function. After sequential
learning with learning rate 0.9 the peak total ozone period (February-May)
concentrations of mean monthly total ozone have been predicted by the two
neural net models. After training and validation, both of the models are found
skillful. But, Two-hidden-layer Perceptron is found to be more adroit in
predicting the mean monthly total ozone concentrations over the aforesaid
period.


title: Optically Controlled Jitter Generator

abstract:
  A new simple circuit producing random pulse trains is proposed and
experimentally studied. The circuit is composed of an operational amplifier and
two feedback links, one of which comprises two photodiodes. The photodiodes are
responsible for nonlinearity in the feedback. By varying the illumination it is
possible to control the nonlinearity in the photodiode current-voltage
characteristics and change the degree of randomness in the oscillations. The
circuit's simplicity and optical control make it attractive for coupled map
lattices.


title:
Heavy particle concentration in turbulence at dissipative and inertial
  scales

abstract:
  Spatial distributions of heavy particles suspended in an incompressible
isotropic and homogeneous turbulent flow are investigated by means of high
resolution direct numerical simulations. In the dissipative range, it is shown
that particles form fractal clusters with properties independent of the
Reynolds number. Clustering is there optimal when the particle response time is
of the order of the Kolmogorov time scale $\tau_\eta$. In the inertial range,
the particle distribution is no longer scale-invariant. It is however shown
that deviations from uniformity depend on a rescaled contraction rate, which is
different from the local Stokes number given by dimensional analysis. Particle
distribution is characterized by voids spanning all scales of the turbulent
flow; their signature in the coarse-grained mass probability distribution is an
algebraic behavior at small densities.


title: Comparative Study of Different Discretizations of the $\phi^4$ Model

abstract:
  We examine various recently proposed discretizations of the well-known
$\phi^4$ field theory. We compare and contrast the properties of their
fundamental solutions including the nature of their kink-type solitary waves
and the spectral properties of the linearization around such waves. We study
these features as a function of the lattice spacing $h$, as one deviates from
the continuum limit of $h \to 0$. We then proceed to a more ``stringent''
comparison of the models, by discussing the scattering properties of a
kink-antikink pair for the different discretizations. These collisions are
well-known to possess properties that quite sensitively depend on the initial
speed even at the continuum limit. We examine how typical model behaviors are
modified in the presence (and as a function) of discreteness and attempt to
extract qualitative trends and issue pertinent warnings about some of the
surprising resulting properties.


title:
Domain Wall and Periodic Solutions of Coupled phi4 Models in an External
  Field

abstract:
  Coupled double well (phi4) one-dimensional potentials abound in both
condensed matter physics and field theory. Here we provide an exhaustive set of
exact periodic solutions of a coupled $\phi^4$ model in an external field in
terms of elliptic functions (domain wall arrays) and obtain single domain wall
solutions in specific limits. We also calculate the energy and interaction
between solitons for various solutions. Both topological and nontopological
(e.g. some pulse-like solutions in the presence of a conjugate field) domain
walls are obtained. We relate some of these solutions to the recently observed
magnetic domain walls in certain multiferroic materials and also in the field
theory context wherever possible. Discrete analogs of these coupled models,
relevant for structural transitions on a lattice, are also considered.

categories: nlin.SI cond-mat.stat-mech hep-th nlin.PS


title:
Some General Results for Multi-dimensional Compactonsin Generalized
  N-dimensional KdV Equations

abstract:
  We derive a general theorem relating the energy and momentum with the
velocity of any solitary wave solution of the generalized KdV equation in
$N$-dimensions that follows from an action principle. Further, we show that our
$N$-dimensional Lagrangian formulation leads to a subclass of the equations
discussed recently by Rosenau, Hyman and Staley.


title:
Interpreting non-random signatures in biomedical signals with Lempel-Ziv
  complexity

abstract:
  Lempel-Ziv complexity (LZ) [1] and its variants have been used widely to
identify non-random patterns in biomedical signals obtained across distinct
physiological states. Non-random signatures of the complexity measure can occur
under nonlinear deterministic as well as non-deterministic settings. Surrogate
data testing have also been encouraged in the past in conjunction with
complexity estimates to make a finer distinction between various classes of
processes. In this brief letter, we make two important observations (1)
Non-Gaussian noise at the dynamical level can elude existing surrogate
algorithms namely: Phase-randomized surrogates (FT) amplitude-adjusted Fourier
transform (AAFT) and iterated amplitude adjusted Fourier transform (IAAFT).
Thus any inference nonlinear determinism as an explanation for the
non-randomness is incomplete (2) Decrease in complexity can be observed even
across two linear processes with identical auto-correlation functions. The
results are illustrated with a second-order auto-regressive process with
Gaussian and non-Gaussian innovations. AR (2) processes have been used widely
to model several physiological phenomena, hence their choice. The results
presented encourage cautious interpretation of non-random signatures in
experimental signals using complexity measures.


title:
Vacuum response to cosmic stretching: accelerated Universe and
  prevention of singularity

abstract:
  Spacetime stretching is included in the general relativity alongside with the
spacetime curvature. Response of the vacuum to cosmic stretching is considered
as macroscopic quantum effect. This effect explains the accelerated expansion
of the Universe without resorting to Plank scale. For negative stretching
(collapse) the same effect can prevent formation of singularity. Stretching
effect can be important for a variety of cosmic phenomena, including collisions
of galaxies and local collapses.


title: Joint Entropy Coding and Encryption using Robust Chaos

abstract:
  We propose a framework for joint entropy coding and encryption using Chaotic
maps. We begin by observing that the message symbols can be treated as the
symbolic sequence of a discrete dynamical system. For an appropriate choice of
the dynamical system, we could back-iterate and encode the message as the
initial condition of the dynamical system. We show that such an encoding
achieves Shannon's entropy and hence optimal for compression. It turns out that
the appropriate discrete dynamical system to achieve optimality is the
piecewise-linear Generalized Luroth Series (GLS) and further that such an
entropy coding technique is exactly equivalent to the popular Arithmetic Coding
algorithm. GLS is a generalization of Arithmetic Coding with different modes of
operation.
  GLS preserves the Lebesgue measure and is ergodic. We show that these
properties of GLS enable a framework for joint compression and encryption and
thus give a justification of the recent work of Grangetto et al. and Wen et al.
Both these methods have the obvious disadvantage of the key length being equal
to the message length for strong security. We derive measure preserving
piece-wise non-linear GLS (nGLS) and their skewed cousins, which exhibit Robust
Chaos. We propose a joint entropy coding and encryption framework using
skewed-nGLS and demonstrate Shannon's desired sensitivity to the key parameter.
Potentially, our method could improve the security and key efficiency over
Grangetto's method while still maintaining the total compression ratio. This is
a new area of research with promising applications in communications.


title:
Soft Computing Techniques in combating the complexity of the atmosphere-
  a review

abstract:
  The purpose of the present review is to discuss the role of Soft Computing
techniques in understanding the complexity associated with atmospheric
phenomena and thus developing predictive models. Problems in atmospheric data
analysis are discussed in brief and the relevance of Soft Computing to the
atmospheric data analysis and their advantage over the conventional methods are
also conversed. Applicability of different Soft Computing techniques is
precisely discussed. In the last section, up-to-date literature appraisal is
incorporated.


title:
Spatiotemporal patterns in a DC semiconductor-gas-discharge system:
  stability analysis and full numerical solutions

abstract:
  A system very similar to a dielectric barrier discharge, but with a simple
stationary DC voltage, can be realized by sandwiching a gas discharge and a
high-ohmic semiconductor layer between two planar electrodes. In experiments
this system forms spatiotemporal and temporal patterns spontaneously, quite
similarly to e.g., Rayleigh-Benard convection. Here it is modeled with a simple
discharge model with space charge effects, and the semiconductor is
approximated as a linear conductor. In previous work, this model has reproduced
the phase transition from homogeneous stationary to homogeneous oscillating
states semiquantitatively. In the present work, the formation of spatial
patterns is investigated through linear stability analysis and through
numerical simulations of the initial value problem; the methods agree well.
They show the onset of spatiotemporal patterns for high semiconductor
resistance. The parameter dependence of temporal or spatiotemporal pattern
formation is discussed in detail.


title:
Formation and Evolution of Singularities in Anisotropic Geometric
  Continua

abstract:
  Evolutionary PDEs for geometric order parameters that admit propagating
singular solutions are introduced and discussed. These singular solutions arise
as a result of the competition between nonlinear and nonlocal processes in
various familiar vector spaces. Several examples are given. The motivating
example is the directed self assembly of a large number of particles for
technological purposes such as nano-science processes, in which the particle
interactions are anisotropic. This application leads to the derivation and
analysis of gradient flow equations on Lie algebras. The Riemann structure of
these gradient flow equations is also discussed.


title:
Predicting Pre-monsoon Thunderstorms -A Statistical View through
  Propositional Logic

abstract:
  Thunderstorms very close to a monsoon and not so close to a monsoon are
considered in this analysis. Some important predictors are considered. Pearson
Correlation Coefficient and lag-1 autocorrelation coefficients are calculated
to create necessary universes of discourse for prepositional logic. The purpose
is to make regression analysis more convenient for prediction of the
pre-monsoon thunderstorm weather phenomenon.


title:
Phase space structures and ionization dynamics of hydrogen atom in
  elliptically polarized microwaves

abstract:
  The multiphoton ionization of hydrogen atoms in a strong elliptically
polarized microwave field exhibits complex features that are not observed for
ionization in circular and linear polarized fields. Experimental data reveal
high sensitivity of ionization dynamics to the small changes of the field
polarization. The multidimensional nature of the problem makes widely used
diagnostics of dynamics, such as Poincar\'{e} surfaces of section, impractical.
We analyze the phase space dynamics using finite time stability analysis
rendered by the fast Lyapunov Indicators technique. The concept of
zero--velocity surface is used to initialize the calculations and visualize the
dynamics. Our analysis provides stability maps calculated for the initial
energy at the maximum and below the saddle of the zero-velocity surface. We
estimate qualitatively the dependence of ionization thresholds on the
parameters of the applied field, such as polarization and scaled amplitude.


title: Geometry of intensive scalar dissipation events in turbulence

abstract:
  Maxima of the scalar dissipation rate in turbulence appear in form of sheets
and correspond to the potentially most intensive scalar mixing events. Their
cross-section extension determines a locally varying diffusion scale of the
mixing process and extends the classical Batchelor picture of one mean
diffusion scale. The distribution of the local diffusion scales is analysed for
different Reynolds and Schmidt numbers with a fast multiscale technique applied
to very high-resolution simulation data. The scales take always values across
the whole Batchelor range and beyond. Furthermore, their distribution is traced
back to the distribution of the contractive short-time Lyapunov exponent of the
flow.


title: Polychromatic interface solitons in nonlinear photonic lattices

abstract:
  We demonstrate that interfaces between two nonlinear periodic photonic
lattices offer unique possibilities for controlling nonlinear interaction
between different spectral components of polychromatic light, and a change in
the light spectrum can have a dramatic effect on the propagation along the
interface. We predict the existence of polychromatic surface solitons which
differ fundamentally from their counterparts in infinite lattices.


title:
Semiclassical expansion of parametric correlation functions of the
  quantum time delay

abstract:
  We derive semiclassical periodic orbit expansions for a correlation function
of the Wigner time delay. We consider the Fourier transform of the two-point
correlation function, the form factor $K(\tau,x,y,M)$, that depends on the
number of open channels $M$, a non-symmetry breaking parameter $x$, and a
symmetry breaking parameter $y$. Several terms in the Taylor expansion about
$\tau=0$, which depend on all parameters, are shown to be identical to those
obtained from Random Matrix Theory.


title:
Propagation of videopulse through a thin layer of two-level atoms
  possessing permanent dipole moments

abstract:
  The excitation of a thin layer of two-level permanent dipole moment atoms by
ultimately short (less than field oscillation period) electromagnetic pulses
(videopulse) is observed. The numerical analysis of matter equations free of
rotating wave approximation and relaxation reveals a strong affect of local
field and Stark effect on temporal behavior of transmitted field. Specifically
it is demonstrated that a dense film irradiated by videopulse emits a short
response with a delay much longer even than the characteristic cooperative time
of atom ensemble. It is supposed that the local field in the thin layer of
permanent dipole atoms is able to re-pump the atomic subsystem. The close
analogy to nonlinear pendulum motion is discuused.


title: Loschmidt echo decay from local boundary perturbations

abstract:
  We investigate the sensitivity of the time evolution of semiclassical wave
packets in two-dimensional chaotic billiards with respect to local
perturbations of their boundaries. For this purpose, we address, analytically
and numerically, the time decay of the Loschmidt echo (LE). We find the LE to
decay exponentially in time, with the rate equal to the classical escape rate
from an open billiard obtained from the original one by removing the
perturbation-affected region of its boundary. Finally, we propose a principal
scheme for the experimental observation of the LE decay.


title: Ordinary differential equations which linearize on differentiation

abstract:
  In this short note we discuss ordinary differential equations which linearize
upon one (or more) differentiations. Although the subject is fairly elementary,
equations of this type arise naturally in the context of integrable systems.


title: Solutions of the reflection equations for the $U_q[G_2]$ vertex model

abstract:
  We investigate the possible regular solutions of the boundary Yang-Baxter
equation for the fundamental $U_q[G_2]$ vertex model. We find four distinct
classes of reflection matrices such that half of them are diagonal while the
other half are non-diagonal. The latter are parameterized by two continuous
parameters but only one solution has all entries non-null. The non-diagonal
solutions do not reduce to diagonal ones at any special limit of the
free-parameters.


title:
Recent Developments in Understanding Two-dimensional Turbulence and the
  Nastrom-Gage Spectrum

abstract:
  Two-dimensional turbulence appears to be a more formidable problem than
three-dimensional turbulence despite the numerical advantage of working with
one less dimension. In the present paper we review recent numerical
investigations of the phenomenology of two-dimensional turbulence as well as
recent theoretical breakthroughs by various leading researchers. We also review
efforts to reconcile the observed energy spectrum of the atmosphere (the
spectrum) with the predictions of two-dimensional turbulence and
quasi-geostrophic turbulence.


title: Dynamics on unbounded domains; co-solutions and inheritance of stability

abstract:
  We consider the dynamics of semiflows of patterns on unbounded domains that
are equivariant under a noncompact group action. We exploit the unbounded
nature of the domain in a setting where there is a strong `global' norm and a
weak `local' norm. Relative equilibria whose group orbits are closed manifolds
for a compact group action need not be closed in a noncompact setting; the
closure of a group orbit of a solution can contain `co-solutions'.
  The main result of the paper is to show that co-solutions inherit stability
in the sense that co-solutions of a Lyapunov stable pattern are also stable
(but in a weaker sense). This means that the existence of a single group orbit
of stable relative equilibria may force the existence of quite distinct group
orbits of relative equilibria, and these are also stable. This is in contrast
to the case for finite dimensional dynamical systems where group orbits of
relative equilibria are typically isolated.


title:
Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV
  Equation

abstract:
  We study the zero dispersion limit of the fifth order KdV equations when time
is sufficiently large. In general, the weak limit may be described by an
arbitrary odd number of hyperbolic equations. Unlike the KdV case, these are
non-strictly hyperbolic equations. However, we show that the weak limit is
governed by three hyperbolic equations in a domain in the space-time for all
times bigger than a large time. Outside this domain, the weak limit satisfies a
single hyperbolic equation.


title:
Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving
  Maps

abstract:
  The leading Pollicott-Ruelle resonance is calculated analytically for a
general class of two-dimensional area-preserving maps. Its wave number
dependence determines the normal transport coefficients. In particular, a
general exact formula for the diffusion coefficient D is derived without any
high stochasticity approximation and a new effect emerges: The angular
evolution can induce fast or slow modes of diffusion even in the high
stochasticity regime. The behavior of D is examined for three particular cases:
(i) the standard map, (ii) a sawtooth map, and (iii) a Harper map as an example
of a map with nonlinear rotation number. Numerical simulations support this
formula.


title:
Universal Whitham hierarchy, dispersionless Hirota equations and
  multi-component KP hierarchy

abstract:
  The goal of this paper is to identify the universal Whitham hierarchy of
genus zero with a dispersionless limit of the multi-component KP hierarchy. To
this end, the multi-component KP hierarchy is (re)formulated to depend on
several discrete variables called ``charges''. These discrete variables play
the role of lattice coordinates in underlying Toda field equations. A
multi-component version of the so called differential Fay identity are derived
from the Hirota equations of the $\tau$-function of this ``charged''
multi-component KP hierarchy. These multi-component differential Fay identities
have a well-defined dispersionless limit (the dispersionless Hirota equations).
The dispersionless Hirota equations turn out to be equivalent to the
Hamilton-Jacobi equations for the $S$-functions of the universal Whitham
hierarchy. The differential Fay identities themselves are shown to be a
generating functional expression of auxiliary linear equations for
scalar-valued wave functions of the multi-component KP hierarchy.


title: Resonant eigenstates in quantum chaotic scattering

abstract:
  We study the spectrum of quantized open maps, as a model for the resonance
spectrum of quantum scattering systems. We are particularly interested in open
maps admitting a fractal repeller. Using the ``open baker's map'' as an
example, we numerically investigate the exponent appearing in the Fractal Weyl
law for the density of resonances; we show that this exponent is not related
with the ``information dimension'', but rather the Hausdorff dimension of the
repeller. We then consider the semiclassical measures associated with the
eigenstates: we prove that these measures are conditionally invariant with
respect to the classical dynamics. We then address the problem of classifying
semiclassical measures among conditionally invariant ones. For a solvable
model, the ``Walsh-quantized'' open baker's map, we manage to exhibit a family
of semiclassical measures with simple self-similar properties.


title: Yang-Baxter algebra and generation of quantum integrable models

abstract:
  An operator deformed quantum algebra is discovered exploiting the quantum
Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along
with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra
underlying quantum integrable systems. Three different directions of
application of this algebra in integrable systems depending on different sets
of values of deforming operators are identified. Fixed values on the whole
lattice yield subalgebras linked to standard quantum integrable models, while
the associated Lax operators generate and classify them in an unified way.
Variable values construct a new series of quantum integrable inhomogeneous
models. Fixed but different values at different lattice sites can produce a
novel class of integrable hybrid models including integrable matter-radiation
models and quantum field models with defects, in particular, a new quantum
integrable sine-Gordon model with defect.

categories: nlin.SI cond-mat.stat-mech hep-th math-ph math.MP


title: Superintegrability in the Manev Problem and its Real Form Dynamics

abstract:
  We report here the existence of Ermanno-Bernoulli type invariants for the
Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz
vector whose conservation is characteristic of the Kepler model. If the orbits
are bounded these invariants exist only when a certain rationality condition is
met and thus we have superintegrability only on a subset of initial values. We
analyze real form dynamics of the Manev model and derive that it is always
superintegrable. We also discuss the symmetry algebras of the Manev model and
its real Hamiltonian form.


title: Tamm oscillations in semi-infinite nonlinear waveguide arrays

abstract:
  We demonstrate numerically the existence of nonlinear Tamm oscillations at
the interface between a substrate and one-dimensional waveguide array with both
cubic and saturable, self-focusing and self-defocusing nonlinearity. Light is
trapped in the vicinity of the boundary of the array due to the interplay
between the repulsive edge potential and Bragg reflection inside the array. In
the special case when this potential is linear these oscillations reduce
themselves to surface Bloch oscillations.


title:
Hyperbolic attractor in a system of coupled non-autonomous van der Pol
  oscillators: Numerical test for expanding and contracting cones

abstract:
  We present numerical verification of hyperbolic nature for chaotic attractor
in a system of two coupled non-autonomous van der Pol oscillators (Kuznetsov,
Phys. Rev. Lett., 95, 144101, 2005). At certain parameter values, in the
four-dimensional phase space of the Poincare map a toroidal domain (a direct
product of a circle and a three-dimensional ball) is determined, which is
mapped into itself and contains the attractor we analyze. In accordance with
the computations, in this absorbing domain the conditions of hyperbolicity are
valid, which are formulated in terms of contracting and expanding cones in the
tangent spaces (the vector spaces of the small state perturbations).


title: Oligo-parametric Hierarchical Structure of Complex Systems

abstract:
  We investigate the possible origin of hierarchical structures in complex
systems describable in terms of a finite and small number of parameters which
control the behavioral pattern at each level of organization. We argue that the
limitation on the number of important parameters at each stage is a reflection
of the fact that Thom's classification of catastrophes, i.e., qualitative
changes, involve only a few parameters. In addition, we also point out that
even in systems with a large number of components, only a few may be of
statistically great significance, just as in Zipf's law the quantitative
measure of the important collections is inversely proportional to the rank. We
then consider the concept of relative degeneracies coming from change of
resolving power, at various scales, which too would vindicate the procedure of
coarse-graining in building up hierarchical organizations. We suggest that,
similar to the group-theoretical annihilation of dangling tensor indices due to
symmetry to minimize energy, even in more inexact contexts such as in biology
and the social sciences, similar attempts by the system to reduce frustration
may lead to cluster formation, which are semi-closed, and let leakage
interactions come into play at larger scales.


title:
Gradient Pattern Analysis of Cosmic Structure Formation: Norm and Phase
  Statistics

abstract:
  This paper presents the preliminary results of the characterization of
pattern evolution in the process of cosmic structure formation. We are applying
on N-body cosmological simulations data the technique proposed by Rosa, Sharma
& Valdivia (1999) and Ramos et al. (2000) to estimate the time behavior of
asymmetries in the gradient field. The gradient pattern analysis is a well
tested tool, used to build asymmetrical fragmentation parameters estimated over
a gradient field of an image matrix able to quantify a complexity measure of
nonlinear extended systems. In this investigation we work with the high
resolution cosmological data simulated by the Virgo consortium, in different
time steps, in order to obtain a diagnostic of the spatio-temporal disorder in
the matter density field. We perform the calculations of the gradient vectors
statistics, such as mean, variance, skewness, kurtosis, and correlations on the
gradient field. Our main goal is to determine different dynamical regimes
through the analysis of complex patterns arising from the evolutionary process
of structure formation. The results show that the gradient pattern technique,
specially the statistical analysis of second and third gradient moment, may
represent a very useful tool to describe the matter clustering in the Universe.


title:
Single polymer dynamics in elongational flow and the confluent Heun
  equation

abstract:
  We investigate the non-equilibrium dynamics of an isolated polymer in a
stationary elongational flow. We compute the relaxation time to the
steady-state configuration as a function of the Weissenberg number. A strong
increase of the relaxation time is found around the coil-stretch transition,
which is attributed to the large number of polymer configurations. The
relaxation dynamics of the polymer is solved analytically in terms of a central
two-point connection problem for the singly confluent Heun equation.


title:
Interface localized modes and hybrid lattice solitons in waveguide
  arrays

abstract:
  We discuss the formation of guided modes localized at the interface separat-
ing two different periodic photonic lattices. Employing the effective discrete
model, we analyze linear and nonlinear interface modes and also predict the
existence of stable interface solitons including the hybrid
staggered/unstaggered lattice solitons with the tails belonging to spectral
gaps of different types.


title:
Small-Signal Amplification of Period-Doubling Bifurcations in Smooth
  Iterated Maps

abstract:
  Various authors have shown that, near the onset of a period-doubling
bifurcation, small perturbations in the control parameter may result in much
larger disturbances in the response of the dynamical system. Such amplification
of small signals can be measured by a gain defined as the magnitude of the
disturbance in the response divided by the perturbation amplitude. In this
paper, the perturbed response is studied using normal forms based on the most
general assumptions of iterated maps. Such an analysis provides a theoretical
footing for previous experimental and numerical observations, such as the
failure of linear analysis and the saturation of the gain. Qualitative as well
as quantitative features of the gain are exhibited using selected models of
cardiac dynamics.


title:
Magnetization-induced optical second-harmonic generation and local
  surface plasmons in magnetic $Co_x Ag_{1-x}$ nanogranular films

abstract:
  Spectroscopy of magnetization-induced second-harmonic generation (MSHG) is
studied in magnetic Co$_{x}$Ag$_{1-x}$ granular films containing Co
nanoparticles. A strong resonance of the magnetic contrast of the
second-harmonic generation (SHG) intensity is observed in the two-photon energy
range from 3,8 eV to 4,5 eV. The local surface plasmons exited in magnetic Co
nanogranules in this spectral range assist MSHG and are responsible for a
significant enhancement of the SHG magnetic contrast due to the resonances of
local optical fields.


title: Emergence is coupled to scope, not level

abstract:
  Since its application to systems, emergence has been explained in terms of
levels of observation. This approach has led to confusion, contradiction,
incoherence and at times mysticism. When the idea of level is replaced by a
framework of scope, resolution and state, this confusion is dissolved. We find
that emergent properties are determined by the relationship between the scope
of macrostate and microstate descriptions. This establishes a normative
definition of emergent properties and emergence that makes sense of previous
descriptive definitions of emergence. In particular, this framework sheds light
on which classes of emergent properties are epistemic and which are
ontological, and identifies fundamental limits to our ability to capture
emergence in formal systems.


title:
The classification of traveling wave solutions and superposition of
  multi-solutions to Camassa-Holm equation with dispersion

abstract:
  Under the traveling wave transformation, Camassa-Holm equation with
dispersion is reduced to an integrable ODE whose general solution can be
obtained using the trick of one-parameter group. Furthermore combining complete
discrimination system for polynomial, the classifications of all single
traveling wave solutions to the Camassa-Holm equation with dispersion is
obtained. In particular, an affine subspace structure in the set of the
solutions of the reduced ODE is obtained. More general, an implicit linear
structure in Camassa-Holm equation with dispersion is found. According to the
linear structure, we obtain the superposition of multi-solutions to
Camassa-Holm equation with dispersion.


title: Domain Wall and Periodic Solutions of a Coupled phi6 Model

abstract:
  Coupled triple well (phi6) one-dimensional potentials occur in both condensed
matter physics and field theory. Here we provide a set of exact periodic
solutions in terms of elliptic functions (domain wall arrays) and obtain single
domain wall solutions in specific limits. Both topological, nontopological
(e.g. some pulse-like solutions) as well as mixed domain walls are obtained. We
relate these solutions to structural phase transitions in materials with
polarization, shuffle modes and strain. We calculate the energy and the
asymptotic interaction between solitons for various solutions. We also consider
the discrete analog of these coupled models and obtain several single and
periodic domain wall exact solutions.

categories: nlin.SI cond-mat.mtrl-sci hep-th nlin.PS


title:
Multilayered feed forward Artificial Neural Network model to predict the
  average summer-monsoon rainfall in India

abstract:
  In the present research, possibility of predicting average summer-monsoon
rainfall over India has been analyzed through Artificial Neural Network models.
In formulating the Artificial Neural Network based predictive model, three
layered networks have been constructed with sigmoid non-linearity. The models
under study are different in the number of hidden neurons. After a thorough
training and test procedure, neural net with three nodes in the hidden layer is
found to be the best predictive model.


title:
A probe into the chaotic nature of total ozone time series by
  Correlation Dimension method

abstract:
  Present paper deals with mean monthly total ozone concentration over Arosa,
Switzerland. The basic rationale is to investigate the existence of chaos
within the relevant time series. Method of correlation dimension is adopted
here as the research methodology. After a rigorous investigation a low
dimensional chaos is identified within the time series pertaining to mean
monthly total ozone concentration over Arosa, Switzerland.


title:
Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds
  Revisited

abstract:
  We investigate soliton solutions of the Toda hierarchy on a quasi-periodic
finite-gap background by means of the double commutation method and the inverse
scattering transform. In particular, we compute the phase shift caused by a
soliton on a quasi-periodic finite-gap background. Furthermore, we consider
short range perturbations via scattering theory. We give a full description of
the effect of the double commutation method on the scattering data and
establish the inverse scattering transform in this setting.


title: SLE description of the nodal lines of random wave functions

abstract:
  The nodal lines of random wave functions are investigated. We demonstrate
numerically that they are well approximated by the so-called SLE_6 curves which
describe the continuum limit of the percolation cluster boundaries. This result
gives an additional support to the recent conjecture that the nodal domains of
random (and chaotic) wave functions in the semi classical limit are adequately
described by the critical percolation theory. It is also shown that using the
dipolar variant of SLE reduces significantly finite size effects.


title:
On the transient and steady state of mass-conserved reaction diffusion
  systems

abstract:
  Reaction diffusion systems with Turing instability and mass conservation are
studied. In such systems, abrupt decays of stripes follow quasi-stationary
states in sequence. At steady state, the distance between stripes is much
longer than that estimated by linear stability analysis at a homogeneous state
given by alternative stability conditions. We show that there exist systems in
which a one-stripe pattern is solely steady state for an arbitrary size of the
systems. The applicability to cell biology is discussed.


title: A note on elliptic coordinates on the Lie algebra e(3)

abstract:
  We introduce elliptic coordinates on the dual space to the Lie algebra e(3$
and discuss the separability of the Clebsch system in these variables. The
proposed Darboux coordinates on e^*(3) coincide with the usual elliptic
coordinates on the cotangent bundle of the two-dimensional sphere at the zero
value of the corresponding Casimir function.


title:
Geometrical approach for description of the mixed state in multi-well
  potentials

abstract:
  We use so-called geometrical approach in description of transition from
regular motion to chaotic in Hamiltonian systems with potential energy surface
that has several local minima. Distinctive feature of such systems is
coexistence of different types of dynamics (regular or chaotic) in different
wells at the same energy Mixed state reveals unique opportunities in research
of quantum manifestations of classical stochasticity. Application of
traditional criteria for transition to chaos (resonance overlap criterion,
negative curvature criterion and stochastic layer destruction criterion) is
inefficient in case of potentials with complex topology. Geometrical approach
allows considering only configuration space but not phase space when
investigating stability. Trajectories are viewed as geodesics of configuration
space equipped with suitable metric. In this approach all information about
chaos and regularity consists in potential function. The aim of this work is to
determine what details of geometry of potential lead to chaos in Hamiltonian
systems using geometrical approach. Numerical calculations are executed for
potentials that are relevant with lowest umbilical catastrophes.


title: Isochronal synchronization of delay-coupled systems

abstract:
  We consider small network models for mutually delay-coupled systems which
typically do not exhibit stable isochronally synchronized solutions. We show
that for certain coupling architectures which involve delayed self feedback to
the nodes, the oscillators become isochronally synchronized. Applications are
shown for both incoherent pump coupled lasers and spatio-temporal coupled fiber
ring lasers.


title:
Two-dimensional periodic waves in a supersonic flow of a Bose-Einstein
  condensate

abstract:
  Stationary periodic solutions of the two-dimensional Gross-Pitaevskii
equation are obtained and analyzed for different parameter values in the
context of the problem of a supersonic flow of a Bose-Einstein condensate past
an obstacle. The asymptotic connections with the corresponding periodic
solutions of the Korteweg-de Vries and nonlinear Schr\"odinger equations are
studied and typical spatial wave distributions are discussed.


title:
Thresholds for breather solutions on the Discrete Nonlinear
  Schr\"odinger Equation with saturable and power nonlinearity

abstract:
  We consider the question of existence of periodic solutions (called breather
solutions or discrete solitons) for the Discrete Nonlinear Schr\"odinger
Equation with saturable and power nonlinearity. Theoretical and numerical
results are proved concerning the existence and nonexistence of periodic
solutions by a variational approach and a fixed point argument. In the
variational approach we are restricted to DNLS lattices with Dirichlet boundary
conditions. It is proved that there exists parameters (frequency or
nonlinearity parameters) for which the corresponding minimizers satisfy
explicit upper and lower bounds on the power. The numerical studies performed
indicate that these bounds behave as thresholds for the existence of periodic
solutions. The fixed point method considers the case of infinite lattices.
Through this method, the existence of a threshold is proved in the case of
saturable nonlinearity and an explicit theoretical estimate which is
independent on the dimension is given. The numerical studies, testing the
efficiency of the bounds derived by both methods, demonstrate that these
thresholds are quite sharp estimates of a threshold value on the power needed
for the the existence of a breather solution. This it justified by the
consideration of limiting cases with respect to the size of the nonlinearity
parameters and nonlinearity exponents.


title:
Regularity properties of critical invariant circles of twist maps, and
  their universality

abstract:
  We compute accurately the golden critical invariant circles of several
area-preserving twist maps of the cylinder. We define some functions related to
the invariant circle and to the dynamics of the map restricted to the circle
(for example, the conjugacy between the circle map giving the dynamics on the
invariant circle and a rigid rotation on the circle). The global H\"older
regularities of these functions are low (some of them are not even once
differentiable). We present several conjectures about the universality of the
regularity properties of the critical circles and the related functions. Using
a Fourier analysis method developed by R. de la Llave and one of the authors,
we compute numerically the Holder regularities of these functions. Our
computations show that -- withing their numerical accuracy -- these
regularities are the same for the different maps studied. We discuss how our
findings are related to some previous results: (a) to the constants giving the
scaling behavior of the iterates on the critical invariant circle (discovered
by Kadanoff and Shenker); (b) to some characteristics of the singular invariant
measures connected with the distribution of iterates. Some of the functions
studied have pointwise Holder regularity that is different at different points.
Our results give a convincing numerical support to the fact that the points
with different Holder exponents of these functions are interspersed in the same
way for different maps, which is a strong indication that the underlying twist
maps belong to the same universality class.

categories: nlin.CD math.DS math.NA physics.class-ph


title:
A Borel transform method for locating singularities of Taylor and
  Fourier series

abstract:
  Given a Taylor series with a finite radius of convergence, its Borel
transform defines an entire function. A theorem of P\'olya relates the large d
istance behavior of the Borel transform in different directions to
singularities of the original function. With the help of the new asymptotic
interpolation method of van der Hoeven, we show that from the knowledge of a
large number of Taylor coefficients we can identify precisely the location of
such singularities, as well as their type when they are isolated. There is no
risk of getting artefacts with this method, which also gives us access to some
of the singularities beyond the convergence disk. The method can also be
applied to Fourier series of analytic periodic functions and is here tested on
various instances constructed from solutions to the Burgers equation. Large
precision on scaling exponents (up to twenty accurate digits) can be achieved.


title:
The scaling attractor and ultimate dynamics for Smoluchowski's
  coagulation equations

abstract:
  We describe a basic framework for studying dynamic scaling that has roots in
dynamical systems and probability theory. Within this framework, we study
Smoluchowski's coagulation equation for the three simplest rate kernels
$K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar
solutions and all universality classes (domains of attraction) for scaling
limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here
we add to this a complete description of the set of all limit points of
solutions modulo scaling (the scaling attractor) and the dynamics on this limit
set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine
representation formula for eternal solutions of Smoluchowski's equation (Adv.
Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on
the scaling attractor, revealing these dynamics to be conjugate to a continuous
dilation, and chaotic in a classical sense. Furthermore, our study of scaling
limits explains how Smoluchowski dynamics ``compactifies'' in a natural way
that accounts for clusters of zero and infinite size (dust and gel).


title:
Discrete Moser-Veselov Integrators for Spatial and Body Representations
  of Rigid Body Motions

abstract:
  The body and spatial representations of rigid body motion correspond,
respectively, to the convective and spatial representations of continuum
dynamics. With a view to developing a unified computational approach for both
types of problems, the discrete Clebsch approach of Cotter and Holm for
continuum mechanics is applied to derive (i) body and spatial representations
of discrete time models of various rigid body motions and (ii) the discrete
momentum maps associated with symmetry reduction for these motions. For these
problems, this paper shows that the discrete Clebsch approach yields a known
class of explicit variational integrators, called discrete Moser-Veselov (DMV)
integrators. The spatial representation of DMV integrators are Poisson with
respect to a Lie-Poisson bracket for the semi-direct product Lie algebra.
Numerical results are presented which confirm the conservative properties and
accuracy of the numerical solutions.


title: Low dimensional behavior in three-dimensional coupled map lattices

abstract:
  The analysis of one-, two-, and three-dimensional coupled map lattices is
here developed under a statistical and dynamical perspective. We show that the
three-dimensional CML exhibits low dimensional behavior with long range
correlation and the power spectrum follows $1/f$ noise. This approach leads to
an integrated understanding of the most important properties of these universal
models of spatiotemporal chaos. We perform a complete time series analysis of
the model and investigate the dependence of the signal properties by change of
dimension.


title:
Multivariate phase space reconstruction by nearest neighbor embedding
  with different time delays

abstract:
  A recently proposed nearest neighbor based selection of time delays for phase
space reconstruction is extended to multivariate time series, with an iterative
selection of variables and time delays. A case study of numerically generated
solutions of the x- and z coordinates of the Lorenz system, and an application
to heart rate and respiration data, are used for illustration.


title: Stabilizing the intensity of a wave amplified by a beam of particles

abstract:
  The intensity of an electromagnetic wave interacting self-consistently with a
beam of charged particles as in a free electron laser, displays large
oscillations due to an aggregate of particles, called the macro-particle. In
this article, we propose a strategy to stabilize the intensity by re-shaping
the macro-particle. This strategy involves the study of the linear stability
(using the residue method) of selected periodic orbits of a mean-field model.
As parameters of an additional perturbation are varied, bifurcations occur in
the system which have drastic effect on the modification of the self-consistent
dynamics, and in particular, of the macro-particle. We show how to obtain an
appropriate tuning of the parameters which is able to strongly decrease the
oscillations of the intensity without reducing its mean-value.


title:
Simple and efficient generation of gap solitons in Bose-Einstein
  condensates

abstract:
  We suggest an efficient method for generating matter-wave gap solitons in a
repulsive Bose-Einstein condensate, when the gap soliton is formed from a
condensate cloud in a harmonic trap after turning on a one-dimensional optical
lattice. We demonstrate numerically that this approach does not require
preparing the initial atomic wave packet in a specific state corresponding to
the edge of the Brillouin zone of the spectrum, and losses that occur during
the soliton generation process can be suppressed by an appropriate adiabatic
switching of the optical lattice.


title: Fano blockade by a Bose-Einstein condensate in an optical lattice

abstract:
  We study the transport of atoms across a localized Bose-Einstein condensate
in a one-dimensional optical lattice. For atoms scattering off the condensate
we predict total reflection as well as full transmission for certain parameter
values on the basis of an exactly solvable model. The findings of analytical
and numerical calculations are interpreted by a tunable Fano-like resonance and
may lead to interesting applications for blocking and filtering atom beams.


title: Fame Emerges as a Result of Small Memory

abstract:
  A dynamic memory model is proposed in which an agent ``learns'' a new agent
by means of recommendation. The agents can also ``remember'' and ``forget''.
The memory size is decreased while the population size is kept constant.
``Fame'' emerged as a few agents become very well known in expense of the
majority being completely forgotten. The minimum and the maximum of fame change
linearly with the relative memory size. The network properties of the
who-knows-who graph, which represents the state of the system, are
investigated.


title: When is negativity not a problem for the ultra-discrete limit?

abstract:
  The `ultra-discrete limit' has provided a link between integrable difference
equations and cellular automata displaying soliton like solutions. In
particular, this procedure generally turns strictly positive solutions of
algebraic difference equations with positive coefficients into corresponding
solutions to equations involving the "Max" operator. Although it certainly is
the case that dropping these positivity conditions creates potential
difficulties, it is still possible for solutions to persist under the
ultra-discrete limit even in their absence. To recognize when this will occur,
one must consider whether a certain expression, involving a measure of the
rates of convergence of different terms in the difference equation and their
coefficients, is equal to zero. Applications discussed include the solution of
elementary ordinary difference equations, a discretization of the Hirota
Bilinear Difference Equation and the identification of integrals of motion for
ultra-discrete equations.


title:
Maximum complexity distribution of a monodimensional ideal gas out of
  equilibrium

abstract:
  The maximum complexity momentum distribution for an isolated monodimensional
ideal gas out of equilibrium is derived analytically. In a first approximation,
it consists of a double non-overlapping Gaussian distribution. In good
agreement with this result, the numerical simulations of a particular isolated
monodimensional gas, which is abruptly pushed far from equilibrium, shows the
maximum complexity distribution in the decay of the system toward equilibrium.


title: Accelerator dynamics of a fractional kicked rotor

abstract:
  It is shown that the Weyl fractional derivative can quantize an open system.
A fractional kicked rotor is studied in the framework of the fractional
Schrodinger equation. The system is described by the non-Hermitian Hamiltonian
by virtue of the Weyl fractional derivative. Violation of space symmetry leads
to acceleration of the orbital momentum. Quantum localization saturates this
acceleration, such that the average value of the orbital momentum can be a
direct current and the system behaves like a ratchet. The classical counterpart
is a nonlinear kicked rotor with absorbing boundary conditions.


title: Genus-zero Whitham hierarchies in conformal-map dynamics

abstract:
  A scheme for solving quasiclassical string equations is developped to prove
that genus-zero Whitham hierarchies describe the deformations of planar domains
determined by rational conformal maps. This property is applied in normal
matrix models to show that deformations of simply-connected supports of
eigenvalues under changes of coupling constants are governed by genus-zero
Whitham hierarchies.


title: From Neuron to Neural Networks dynamics

abstract:
  This paper presents an overview of some techniques and concepts coming from
dynamical system theory and used for the analysis of dynamical neural networks
models. In a first section, we describe the dynamics of the neuron, starting
from the Hodgkin-Huxley description, which is somehow the canonical description
for the ``biological neuron''. We discuss some models reducing the
Hodgkin-Huxley model to a two dimensional dynamical system, keeping one of the
main feature of the neuron: its excitability. We present then examples of phase
diagram and bifurcation analysis for the Hodgin-Huxley equations. Finally, we
end this section by a dynamical system analysis for the nervous flux
propagation along the axon. We then consider neuron couplings, with a brief
description of synapses, synaptic plasticiy and learning, in a second section.
We also briefly discuss the delicate issue of causal action from one neuron to
another when complex feedback effects and non linear dynamics are involved. The
third section presents the limit of weak coupling and the use of normal forms
technics to handle this situation. We consider then several examples of
recurrent models with different type of synaptic interactions (symmetric,
cooperative, random). We introduce various techniques coming from statistical
physics and dynamical systems theory. A last section is devoted to a detailed
example of recurrent model where we go in deep in the analysis of the dynamics
and discuss the effect of learning on the neuron dynamics. We also present
recent methods allowing the analysis of the non linear effects of the neural
dynamics on signal propagation and causal action. An appendix, presenting the
main notions of dynamical systems theory useful for the comprehension of the
chapter, has been added for the convenience of the reader.


title:
Does the complex susceptibility of the Henon map have a pole in the
  upper-half plane ? A numerical investigation

abstract:
  It has been rigorously shown in [Ruelle, 2005] that the complex
susceptibility of chaotic maps of the interval can have a pole in the
upper-half complex plane. We develop a numerical procedure allowing to exhibit
this pole from time series. We then apply the same analysis to the Henon map
and conjecture that the complex susceptibility has also a pole in the
upper-half complex plane.

categories: nlin.CD cond-mat.stat-mech math-ph math.DS math.MP


title: Phase synchronization in time-delay systems

abstract:
  Though the notion of phase synchronization has been well studied in chaotic
dynamical systems without delay, it has not been realized yet in chaotic
time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In
this article we report the first identification of phase synchronization in
coupled time-delay systems exhibiting hyperchaotic attractor. We show that
there is a transition from non-synchronized behavior to phase and then to
generalized synchronization as a function of coupling strength. These
transitions are characterized by recurrence quantification analysis, by phase
differences based on a new transformation of the attractors and also by the
changes in the Lyapunov exponents. We have found these transitions in coupled
piece-wise linear and in Mackey-Glass time-delay systems.


title:
Experimental realization of strange nonchaotic attractors in a
  quasiperiodically forced electronic circuit

abstract:
  We have identified the three prominent routes, namely Heagy-Hammel,
fractalization and intermittency routes, and their mechanisms for the birth of
strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic
system constructed using a negative conductance series LCR circuit with a diode
both numerically and experimentally. The birth of SNAs by these three routes is
verified from both experimental and their corresponding numerical data by
maximal Lyapunov exponents, and their variance, Poincar\'e maps, Fourier
amplitude spectrum, spectral distribution function and finite-time Lyapunov
exponents. Although these three routes have been identified numerically in
different dynamical systems, the experimental observation of all these
mechanisms is reported for the first time to our knowledge and that too in a
single second order electronic circuit.


title:
A Formal Treatment of Generalized Preferential Attachment and its
  Empirical Validation

abstract:
  Generalized preferential attachment is defined as the tendency of a vertex to
acquire new links in the future with respect to a particular vertex property.
Understanding which properties influence link acquisition tendency (LAT) gives
us a predictive power to estimate the future growth of network and insight
about the actual dynamics governing the complex networks. In this study, we
explore the effect of age and degree on LAT by analyzing data collected from a
new complex-network growth dataset. We found that LAT and degree of a vertex
are linearly correlated in accordance with previous studies. Interestingly, the
relation between LAT and age of a vertex is found to be in conflict with the
known models of network growth. We identified three different periods in the
network's lifetime where the relation between age and LAT is strongly positive,
almost stationary and negative correspondingly.

categories: nlin.AO cond-mat.stat-mech cs.CY physics.data-an


title: Self-Interacting Electron as a Nonlinear Dynamical System

abstract:
  We have proposed a simple one-dimensional model of internal particle
dynamics. The model is based on the assumption that self-interaction can be
represented by a nonlinear feedback and described by a quadratic recurrent map.
Charge plays the role of a generalized dynamical variable and a feedback
coupling parameter. The model suggests that charge and action quantization stem
from the system's dissipative quality and from a hierarchy of supercycle orbits
located between period-doubling bifurcations on the Feigenbaum tree. Among the
numerical results, we have discovered a link between the quantum of action and
the elementary charge. We also found that the fine structure constant can with
a good accuracy be expressed exclusively through mathematical constants,
including the Feigenbaum delta. We have introduced dimensionless numbers that
describe the relative role of the internal particle dynamics when both internal
and external dynamics are taken into consideration. We have found these numbers
to be close to the electron, proton, and neutron g-factors known from the
experiment.


title: Seed and soliton solutions for Adler's lattice equation

abstract:
  Adler's lattice equation has acquired the status of a master equation among
2D discrete integrable systems. In this paper we derive what we believe are the
first explicit solutions of this equation. In particular it turns out necessary
to establish a non-trivial seed solution from which soliton solutions can
subsequently be constructed using the B\"acklund transformation. As a corollary
we find the corresponding solutions of the Krichever-Novikov equation which is
obtained from Adler's equation in a continuum limit.