title: On a theorem by Treves

abstract:
  According to a theorem of Treves, the conserved functionals of the KdV
equation vanish on each formal Laurent series 1/x^2 + u0 + u2 x^2 + u3 x^3 +
>... . We propose a new, very simple geometrical proof for this statement.


title: Controlling chaos in area-preserving maps

abstract:
  We describe a method of control of chaos that occurs in area-preserving maps.
This method is based on small modifications of the original map by addition of
a small control term. We apply this control technique to the standard map and
to the tokamap.


title:
A relationship between rational and multi-soliton solutions of the BKP
  hierarchy

abstract:
  We consider a special class of solutions of the BKP hierarchy which we call
$\tau$-functions of hypergeometric type. These are series in Schur
$Q$-functions over partitions, with coefficients parameterised by a function of
one variable $\xi$, where the quantities $\xi(k)$, $k\in\mathbb{Z^+}$, are
integrals of motion of the BKP hierarchy. We show that this solution is, at the
same time, a infinite soliton solution of a dual BKP hierarchy, where the
variables $\xi(k)$ are now related to BKP higher times. In particular, rational
solutions of the BKP hierarchy are related to (finite) multi-soliton solution
of the dual BKP hierarchy. The momenta of the solitons are given by the parts
of partitions in the Schur $Q$-function expansion of the $\tau$-function of
hypergeometric type. We also show that the KdV and the NLS soliton
$\tau$-functions coinside the BKP $\tau$-functions of hypergeometric type,
evaluated at special point of BKP higher time; the variables $\xi$ (which are
BKP integrals of motions) being related to KdV and NLS higher times.


title: Tailoring Phase Space : A Way to Control Hamiltonian Transport

abstract:
  We present a method to control transport in Hamiltonian systems. We provide
an algorithm - based on a perturbation of the original Hamiltonian localized in
phase space - to design small control terms that are able to create isolated
barriers of transport without modifying other parts of phase space. We apply
this method of localized control to a forced pendulum model and to a system
describing the motion of charged particles in a model of turbulent electric
field.


title: Evolution of Robust Developmental Neural Networks

abstract:
  We present the first evolved solutions to a computational task within the
Neuronal Organism Evolution model (Norgev) of artificial neural network
development. These networks display a remarkable robustness to external noise
sources, and can regrow to functionality when severely damaged. In this
framework, we evolved a doubling of network functionality (double-NAND
circuit). The network structure of these evolved solutions does not follow the
logic of human coding, and instead more resembles the decentralized dendritic
connection pattern of more biological networks such as the 'C. elegans' brain.


title: Individual strategies in complementarity games and population dynamics

abstract:
  We introduce and study an evolutionary complementarity game where in each
round a player of population 1 is paired with a member of population 2. The
game is symmetric, and each player tries to obtain an advantageous deal, but
when one of them pushes too hard, no deal at all can be concluded, and they
both loose. The game has many equilibria, and which of them is reached depends
on the history of the interactions as the players evolve according to a fitness
function that measures their gains across the interactions. We can then break
the symmetry by assigning different strategy spaces to the populations, varying
in particular with respect to the information available to the agents. The
agents can, for example, adapt to the behavior of their opponents met in
previous rounds, or they can try to copy the strategies of their successful
friends. It turns out that, in general, the more restricted strategy spaces,
that is, those that utilize less information, are more advantageous for a
population as a whole as their adoption drives the equilibrium in a direction
advantageous to that population. One reason is that a simpler strategy can be
learned faster in an evolutionary setting, another is that it is good for a
population to have some individuals that are unfit in the sense that they make
offers that are individually unsuccessful, but have a systematic effect on the
strategies of their opponents. All these effects are demonstrated through
systematic simulations.


title: 1/f noise in the Two-Body Random Ensemble

abstract:
  We show that the spectral fluctuations of the Two-Body Random Ensemble (TBRE)
exhibit 1/f noise. This result supports a recent conjecture stating that
chaotic quantum systems are characterized by 1/f noise in their energy level
fluctuations. After suitable individual averaging, we also study the
distribution of the exponent \alpha in the 1/f^{\alpha} noise for the
individual members of the ensemble. Almost all the exponents lie inside a
narrow interval around \alpha=1 suggesting that also individual members exhibit
1/f noise, provided they are individually unfolded

categories: nlin.CD cond-mat.mes-hall cond-mat.stat-mech nucl-th


title:
Stabilizing near-nonhyperbolic chaotic systems and its potential
  applications in neuroscience

abstract:
  Based on the invariance principle of differential equations a simple,
systematic, and rigorous feedback scheme with the variable feedback strength is
proposed to stabilize nonlinearly any chaotic systems without any prior
analytical knowledge of the systems. Especially the method may be used to
control near-nonhyperbolic chaotic systems, which although arising naturally
from models in astrophysics to those for neurobiology, all OGY-type methods
will fail to stabilize. The technique is successfully used to the famous
Hindmarsh-Rose model neuron and the R$\ddot{\textrm{o}}$ssler hyperchaos
system.


title:
A simple adaptive-feedback controller for high-quality chaos
  synchronization

abstract:
  Based on the invariance principle of differential equations, a simple
adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic
systems. Unlike the usual linear feedback, the variable feedback strength is
automatically adapted to completely synchronize two almost arbitrary identical
chaotic systems, so this scheme is analytical, and simple to implement in
practice. Moreover it is quite robust against the effect of noise. The famous
Lorenz and R$\ddot{\textrm{o}}$ssler hyperchaos systems are used as
illustrative examples.


title: Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

abstract:
  Identifying causal relations among simultaneously acquired signals is an
important problem in multivariate time series analysis. For linear stochastic
systems Granger proposed a simple procedure called the Granger causality to
detect such relations. In this work we consider nonlinear extensions of
Granger's idea and refer to the result as Extended Granger Causality. A simple
approach implementing the Extended Granger Causality is presented and applied
to multiple chaotic time series and other types of nonlinear signals. In
addition, for situations with three or more time series we propose a
conditional Extended Granger Causality measure that enables us to determine
whether the causal relation between two signals is direct or mediated by
another process.


title: Optical pulse propagation in fibers with random dispersion

abstract:
  The propagation of optical pulses in two types of fibers with randomly
varying dispersion is investigated. The first type refers to a uniform fiber
dispersion superimposed by random modulations with a zero mean. The second type
is the dispersion-managed fiber line with fluctuating parameters of the
dispersion map. Application of the mean field method leads to the nonlinear
Schr\"odinger equation (NLSE) with a dissipation term, expressed by a 4th order
derivative of the wave envelope. The prediction of the mean field approach
regarding the decay rate of a soliton is compared with that of the perturbation
theory based on the Inverse Scattering Transform (IST). A good agreement
between these two approaches is found. Possible ways of compensation of the
radiative decay of solitons using the linear and nonlinear amplification are
explored. Corresponding mean field equation coincides with the complex
Swift-Hohenberg equation. The condition for the autosolitonic regime in
propagation of optical pulses along a fiber line with fluctuating dispersion is
derived and the existence of autosoliton (dissipative soliton) is confirmed by
direct numerical simulation of the stochastic NLSE. The dynamics of solitons in
optical communication systems with random dispersion-management is further
studied applying the variational principle to the mean field NLSE, which
results in a system of ODE's for soliton parameters. Extensive numerical
simulations of the stochastic NLSE, mean field equation and corresponding set
of ODE's are performed to verify the predictions of the developed theory.


title: The averaging of weakly nonlocal Symplectic Structures

abstract:
  We consider the averaging of the weakly nonlocal Symplectic Structures
corresponding to local evolution PDE's in the Whitham method. The averaging
procedure gives the weakly nonlocal Symplectic Structure of Hydrodynamic Type
for the corresponding Whitham system. The procedure gives also the "action
variables" corresponding to the wave numbers of $m$-phase solutions of initial
system which give the additional conservation laws for the Whitham system.


title: Bifurcations and stability of gap solitons in periodic potentials

abstract:
  We analyze the existence, stability, and internal modes of gap solitons in
nonlinear periodic systems described by the nonlinear Schrodinger equation with
a sinusoidal potential, such as photonic crystals, waveguide arrays,
optically-induced photonic lattices, and Bose-Einstein condensates loaded onto
an optical lattice. We study bifurcations of gap solitons from the band edges
of the Floquet-Bloch spectrum, and show that gap solitons can appear near all
lower or upper band edges of the spectrum, for focusing or defocusing
nonlinearity, respectively. We show that, in general, two types of gap solitons
can bifurcate from each band edge, and one of those two is always unstable. A
gap soliton corresponding to a given band edge is shown to possess a number of
internal modes that bifurcate from all band edges of the same polarity. We
demonstrate that stability of gap solitons is determined by location of the
internal modes with respect to the spectral bands of the inverted spectrum and,
when they overlap, complex eigenvalues give rise to oscillatory instabilities
of gap solitons.


title:
Coupled Chaotic Oscillators and Its Relation with Artificial Quadrupeds'
  Central Pattern Generator

abstract:
  Animal locomotion employs different periodic patterns known as animal gaits.
In 1993 Collins and Stewart achieved the characterization in quadrupeds and
bipeds by using permutation symmetries groups which impose constrains in the
locomotion centre called Central Generator Pattern (CGP) in the animal brain.
They modelled the CGP by coupling four non linear oscillators and with the only
change in the coupling it is possible to reproduce all the gaits. In this work
we propose to use coupled chaotic oscillators synchronized with the Pyragas
method not only to characterize the CGP symmetries but also evaluate the time
serie behaviour when the foot is in contact with the ground for futures robotic
applications.


title:
An integrable $U_q(\hat{gl}(2|2))_1$-Model: Corner Transfer Matrices and
  Young Skew Diagrams

abstract:
  The path space of an inhomogeneous vertex model constructed from the vector
representation of $U_q\bigl(gl(2|2)\bigr)$ and its dual is studied for various
choices of composite vertices and assignments of $gl(2|2)$-weights. At $q=0$,
the corner transfer matrix Hamiltonian acts trigonally on the space of
half-infinite configurations subject to a particular boundary condition. A
weight-preserving one-to-one correspondence between the half-infinite
configurations and the weight states of a level-one module of
$U_q\bigl(\hat{sl}(2|2)\bigr)/{\cal H}$ with grade $-n$ is found for $n\geq-3$
if the grade $-n$ is identified with the diagonal element of the CTM
Hamiltonian. In each case, the module can be decomposed into two irreducible
level-one modules, one of them including infinitely many weight states at fixed
grade. Based on a mapping of the path space onto pairs of border stripes, the
character of the reducible module is decomposed in terms of skew Schur
functions. Relying on an explicit verification for simple border stripes, a
correspondence between the paths and level-zero modules of
$U_q\bigl(\hat{sl}(2|2)\bigr)$ constructed from an infinite-dimensional
$U_q\bigl(gl(2|2)\bigr)$-module is conjectured.


title: The Polymer Stress Tensor in Turbulent Shear Flows

abstract:
  The interaction of polymers with turbulent shear flows is examined. We focus
on the structure of the elastic stress tensor, which is proportional to the
polymer conformation tensor. We examine this object in turbulent flows of
increasing complexity. First is isotropic turbulence, then anisotropic (but
homogenous) shear turbulence and finally wall bounded turbulence. The main
result of this paper is that for all these flows the polymer stress tensor
attains a universal structure in the limit of large Deborah number $\De\gg 1$.
We present analytic results for the suppression of the coil-stretch transition
at large Deborah numbers. Above the transition the turbulent velocity
fluctuations are strongly correlated with the polymer's elongation: there
appear high-quality "hydro-elastic" waves in which turbulent kinetic energy
turns into polymer potential energy and vice versa. These waves determine the
trace of the elastic stress tensor but practically do not modify its universal
structure. We demonstrate that the influence of the polymers on the balance of
energy and momentum can be accurately described by an effective polymer
viscosity that is proportional to to the cross-stream component of the elastic
stress tensor. This component is smaller than the stream-wise component by a
factor proportional to $\De ^2 $. Finally we tie our results to wall bounded
turbulence and clarify some puzzling facts observed in the problem of drag
reduction by polymers.


title: Analytical approach to soliton ratchets in asymmetric potentials

abstract:
  We use soliton perturbation theory and collective coordinate ansatz to
investigate the mechanism of soliton ratchets in a driven and damped asymmetric
double sine-Gordon equation. We show that, at the second order of the
perturbation scheme, the soliton internal vibrations can couple {\it
effectively}, in presence of damping, to the motion of the center of mass,
giving rise to transport. An analytical expression for the mean velocity of the
soliton is derived. The results of our analysis confirm the internal mode
mechanism of soliton ratchets proposed in [Phys. Rev. E {\bf 65} 025602(R)
(2002)].

categories: nlin.SI cond-mat.soft math-ph math.MP nlin.PS


title: Characteristics of a Delayed System with Time-dependent Delay Time

abstract:
  The characteristics of a time-delayed system with time-dependent delay time
is investigated. We demonstrate the nonlinearity characteristics of the
time-delayed system are significantly changed depending on the properties of
time-dependent delay time and especially that the reconstructed phase
trajectory of the system is not collapsed into simple manifold, differently
from the delayed system with fixed delay time. We discuss the possibility of a
phase space reconstruction and its applications.


title:
Map representation of the time-delayed system in the presence of Delay
  Time Modulation: an Application to the stability analysis

abstract:
  We introduce the map representation of a time-delayed system in the presence
of delay time modulation. Based on this representation, we find the method by
which to analyze the stability of that kind of a system. We apply this method
to a coupled chaotic system and discuss the results in comparison to the system
with a fixed delay time.


title:
A Cross-Over in the Enstrophy Decay in Two-Dimensional Turbulence in a
  Finite Box

abstract:
  The numerical simulation of two-dimensional decaying turbulence in a large
but finite box presented in this paper uncovered two physically different
regimes of enstrophy decay. During the initial stage, the enstrophy, generated
by a random Gaussian initial condition, decays as t^{-gamma} with gamma
approximately 0.7-0.8. After that, the flow undergoes a transition to a gas or
fluid composed of distinct vortices. Simultaneously, the magnitude of the decay
exponent crosses over to gamma approximately 0.4. An exact relation for the
total number of vortices, N(t), in terms of the mean circulation of an
individual vortex is derived. A theory predicting that N(t) is proportional to
t^{-xi} and the magnitudes of exponents gamma=2/5 and xi=4/5 is presented and
the possibility of an additional very late-time cross-over to gamma=1/3 and
xi=2/3 is also discussed.


title: Random maps in physical systems

abstract:
  We show that functions of type $X_n = P[Z^n]$, where $P[t]$ is a periodic
function and $Z$ is a generic real number, can produce sequences such that any
string of values $X_{s}, X_{s+1}, ...,X_{s+m}$ is deterministically independent
of past and future values. There are no correlations between any values of the
sequence. We show that this kind of dynamics can be generated using a recently
constructed optical device composed of several Mach--Zehnder interferometers.
Quasiperiodic signals can be transformed into random dynamics using nonlinear
circuits. We present the results of real experiments with nonlinear circuits
that simulate exponential and sine functions.


title:
S-functions, reductions and hodograph solutions of the r-th
  dispersionless modified KP and Dym hierarchies

abstract:
  We introduce an S-function formulation for the recently found r-th
dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also
a connection of these $S$-functions with the Orlov functions of the
hierarchies. Then, we discuss a reduction scheme for the hierarchies that
together with the $S$-function formulation leads to hodograph systems for the
associated solutions. We consider also the connection of these reductions with
those of the dispersionless KP hierarchy and with hydrodynamic type systems. In
particular, for the 1-component and 2-component reduction we derive, for both
hierarchies, ample sets of examples of explicit solutions.


title:
Rotating waves in the Theta model for a ring of synaptically connected
  neurons

abstract:
  We study rotating waves in the Theta model for a ring of
synaptically-interacting neurons. We prove that when the neurons are
oscillatory, at least one rotating wave always exists. In the case of excitable
neurons, we prove that no travelling waves exist when the synaptic coupling is
weak, and at least two rotating waves, a `fast' one and a `slow' one, exist
when the synaptic coupling is sufficiently strong. We derive explicit upper and
lower bounds for the `critical' coupling strength as well as for wave
velocities. We also study the special case of uniform coupling, in which
complete analytical results on the rotating waves can be achieved.


title:
Generalized Phase Synchronization in unidirectionally coupled chaotic
  oscillators

abstract:
  We investigate phase synchronization between two identical or detuned
response oscillators coupled to a slightly different drive oscillator. Our
result is that phase synchronization can occur between response oscillators
when they are driven by correlated (but not identical) inputs from the drive
oscillator. We call this phenomenon Generalized Phase Synchronization (GPS) and
clarify its characteristics using Lyapunov exponents and phase difference
plots.


title:
Directed anomalous diffusion without a biased field: A ratchet
  accelerator

abstract:
  Directed classical current that increases linearly with time without using a
biased external field is obtained in a simple model Hamiltonian system derived
from a modified kicked rotor model, by breaking the spatial symmetry of the
transporting regular islands in the classical phase space. A parallel study of
the corresponding quantum dynamics suggests that although quantum coherence
effects suppress the directed current and can even induce a current reversal,
directed quantum current that increases linearly with time can nonetheless be
realized in a quantum system that is far from the classical limit.


title:
Origin of the Transition Inside the Desynchronized State in Coupled
  Chaotic Oscillators

abstract:
  We investigate the origin of the transition inside the desynchronization
state via phase jumps in coupled chaotic oscillators. We claim that the
transition is governed by type-I intermittency in the presence of noise whose
characteristic relation is $<l > \propto \exp(\alpha|\epsilon_t
-\epsilon|^{3/2})$ for $\epsilon_t -\epsilon <0$ and $<l > \propto (\epsilon_t
-\epsilon)^{-1/2}$ for $\epsilon_t -\epsilon >0$, where $<l>$ is the average
length of the phase locking state and $\epsilon$ is the coupling strength. To
justify our claim we obtain analytically the tangent point, the bifurcation
point, and the return map which agree well with those of the numerical
simulations.


title:
Maximum Drag Reduction Asymptotes and the Cross-Over to the Newtonian
  Plug

abstract:
  We employ the full FENE-P model of hydrodynamics of a dilute polymer
solutions to derive a theoretical approach to drag reduction in wall bounded
turbulence. We recapture the results of a recent simplified theory which
derived the universal Maximum Drag Reduction (MDR) asymptote, and complement
that theory with a discussion of the cross-over from the MDR to the Newtonian
plug when the drag reduction saturates. The FENE-P model gives rise to a rather
complex theory due to the interaction of the velocity field with the polymeric
conformation tensor, making analytic estimates quite taxing. To overcome this
we develop the theory in a computer-assisted manner, checking at each point the
analytic estimates by Direct Numerical Simulations (DNS) of viscoelastic
turbulence in a channel.


title:
On reductions of some KdV-type systems and their link to the quartic
  He'non-Heiles Hamiltonian

abstract:
  A few 2+1-dimensional equations belonging to the KP and modified KP
hierarchies are shown to be sufficient to provide a unified picture of all the
integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.


title:
Symmetries and Integrability Properties of Generalized Fisher Type
  Nonlinear Diffusion Equation

abstract:
  Nonlinear reaction-diffusion systems are known to exhibit very many novel
spatiotemporal patterns. Fisher equation is a prototype of diffusive equations.
In this contribution we investigate the integrability properties of the
generalized Fisher type equation to obtain physically interesting solutions
using Lie symmetry analysis. In particular, we report several travelling wave
patterns, static patterns and localized structures depending upon the choice of
the parameters involved.


title: Slowdown and splitting of gap solitons in apodized Bragg gratings

abstract:
  We study the motion of gap solitons in two models of apodized nonlinear fiber
Bragg gratings (BGs), with the local reflectivity (LR) varying along the fiber.
A single step of LR, and a periodic array of alternating steps with opposite
signs (a "Bragg superstructure") are considered. A challenging possibility is
to slow down and eventually halt the soliton by passing it through the step of
increasing reflectivity, thus capturing a pulse of standing light. First, we
develop an analytical approach, assuming adiabatic evolution of the soliton,
and making use of the energy conservation and balance equation for the
momentum. Comparison with simulations shows that the analytical approximation
is quite accurate (unless the inhomogeneity is too steep): the soliton is
either transmitted across the step or bounces back. If the step is narrow,
systematic simulations demontrate that the soliton splits into transmitted and
reflected pulses (splitting of a BG soliton which hits a chirped grating was
observed in experiments). Moving through the periodic "superstructure", the
soliton accummulates distortion and suffers radiation loss if the structure is
composed of narrow steps. The soliton moves without any loss or irreversible
deformation through the array of sufficiently broad steps.


title: Regularization of the collision in the electromagnetic two-body problem

abstract:
  We derive a differential equation that is regular at the collision of two
equal-mass bodies with attractive interaction in the relativistic
action-at-a-distance electrodynamics. Our method uses the energy constant
related to the Poincar\'{e} invariance of the theory to motivate the
regularizing coordinate transformation and to remove infinities from the
equation of motion. The collision orbits are calculated numerically using the
regular equation adapted in a self-consistent minimization method (a stable
numerical method that chooses only nonrunaway solutions). This dynamical system
appeared 100 years ago as a time-symmetric relativistic motion and aquired the
status of electrodynamics in the 1940's by the works of Dirac, Wheeler and
Feynman. We outline the method with an emphasis on the physics of this complex
conservative dynamical system.


title: When Chaos Meets Computers

abstract:
  This paper focuses on an interesting phenomenon when chaos meets computers.
It is found that digital computers are absolutely incapable of showing true
long-time dynamics of some chaotic systems, including the tent map, the
Bernoulli shift map and their analogues, even in a high-precision
floating-point arithmetic. Although the results cannot directly generalized to
most chaotic systems, the risk of using digital computers to numerically study
continuous dynamical systems is shown clearly. As a result, we reach the old
saying that "it is impossible to do everything with computers only".


title: Energy Localization in the Peyrard-Bishop DNA model

abstract:
  We study energy localization on the oscillator-chain proposed by Peyrard and
Bishop to model the DNA. We search numerically for conditions with initial
energy in a small subgroup of consecutive oscillators of a finite chain and
such that the oscillation amplitude is small outside this subgroup for a long
timescale. We use a localization criterion based on the information entropy and
we verify numerically that such localized excitations exist when the nonlinear
dynamics of the subgroup oscillates with a frequency inside the reactive band
of the linear chain. We predict a mimium value for the Morse parameter $(\mu
>2.25)$ (the only parameter of our normalized model), in agreement with the
numerical calculations (an estimate for the biological value is $\mu =6.3$).
For supercritical masses, we use canonical perturbation theory to expand the
frequencies of the subgroup and we calculate an energy threshold in agreement
with the numerical calculations.


title:
New Integrable Hierarchies from Vertex Operator Representations of
  Polynomial Lie Algebras

abstract:
  We give a representation--theoretic interpretation of recent discovered
coupled soliton equations using vertex operators construction of affinization
of not simple but quadratic Lie algebras. In this setup we are able to obtain
new integrable hierarchies coupled to each Drinfeld--Sokolov of $A$, $B$, $C$,
$D$ hierarchies and to construct their soliton solutions.


title: Social Balance Theory

abstract:
  We construct a model based on social balance theory proposed by Fritz Heider
to analyze the interpersonal network among social agents. The model of social
balance theory provides us an interesting tool to see how a social group
evolves to the possible balance state. We introduce the balance index that can
be used to measure social balance in macro structure level (global balance
index) or in micro structure (local balance index) to see how the local balance
index influences the global balance structure. Several experiments are done and
we discover how the social group can form separation of subgroups in a group or
strengthening a social group while emphasizing the structure theorem and social
mitosis previously introduced.


title:
Singularity Structure, Symmetries and Integrability of Generalized
  Fisher Type Nonlinear Diffusion Equation

abstract:
  In this letter, the integrability aspects of a generalized Fisher type
equation with modified diffusion in (1+1) and (2+1) dimensions are studied by
carrying out a singularity structure and symmetry analysis. It is shown that
the Painlev\'e property exists only for a special choice of the parameter
($m=2$). A B\"acklund transformation is shown to give rise to the linearizing
transformation to the linear heat equation for this case ($m=2$). A Lie
symmetry analysis also picks out the same case ($m=2$) as the only system among
this class as having nontrivial infinite dimensional Lie algebra of symmetries
and that the similarity variables and similarity reductions lead in a natural
way to the linearizing transformation and physically important classes of
solutions (including known ones in the literature), thereby giving a group
theoretical understanding of the system. For nonintegrable cases in (2+1)
dimensions, associated Lie symmetries and similarity reductions are indicated.


title: Nonlocal incoherent solitons

abstract:
  We investigate the propagation of partially coherent beams in spatially
nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive
analytical formulas for the evolution of the beam parameters and conditions for
the formation of nonlocal incoherent solitons.


title:
On the Integrability, B\"Acklund Transformation and Symmetry Aspects of
  a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

abstract:
  The dynamics of nonlinear reaction-diffusion systems is dominated by the
onset of patterns and Fisher equation is considered to be a prototype of such
diffusive equations. Here we investigate the integrability properties of a
generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e
singularity structure analysis singles out a special case ($m=2$) as
integrable. More interestingly, a B\"acklund transformation is shown to give
rise to a linearizing transformation for the integrable case. A Lie symmetry
analysis again separates out the same $m=2$ case as the integrable one and
hence we report several physically interesting solutions via similarity
reductions. Thus we give a group theoretical interpretation for the system
under study. Explicit and numerical solutions for specific cases of
nonintegrable systems are also given. In particular, the system is found to
exhibit different types of travelling wave solutions and patterns, static
structures and localized structures. Besides the Lie symmetry analysis,
nonclassical and generalized conditional symmetry analysis are also carried
out.


title:
Sidebranch Structures of Dendritic Patterns in a Coupled Map Lattice
  Model

abstract:
  Dendrites with developed sidebranches are numerically studied with a coupled
map lattice model. The competitive dynamics among sidebranches determines the
shape of the envelope. The envelope has a parabolic shape near the tip of the
dendrite and the envelope angle with respect to the main branch increases up to
45$^{\circ}$ finally. In an intermediate region, the envelope grows roughly in
a power law, however, the exponent increases gradually as a function of the
distance from the tip. The competitive dynamics among many branches is also
observed in a unidirectional growth from a linear seed, and it is compared with
the competitive dynamics of sidebranches.


title:
Synchronization Based Approach for Estimating All Model Parameters of
  Chaotic Systems

abstract:
  The problem of dynamic estimation of all parameters of a model representing
chaotic and hyperchaotic systems using information from a scalar measured
output is solved. The variational calculus based method is robust in the
presence of noise, enables online estimation of the parameters and is also able
to rapidly track changes in operating parameters of the experimental system.
The method is demonstrated using the Lorenz, Rossler chaos and hyperchaos
models. Its possible application in decoding communications using chaos is
discussed.


title:
Logarithmic periodicities in the bifurcations of type-I intermittent
  chaos

abstract:
  The critical relations for statistical properties on saddle-node bifurcations
are shown to display undulating fine structure, in addition to their known
smooth dependence on the control parameter. A piecewise linear map with the
type-I intermittency is studied and a log-periodic dependence is numerically
obtained for the average time between laminar events, the Lyapunov exponent and
attractor moments. The origin of the oscillations is built in the natural
probabilistic measure of the map and can be traced back to the existence of
logarithmically distributed discrete values of the control parameter giving
Markov partition. Reinjection and noise effect dependences are discussed and
indications are given on how the oscillations are potentially applicable to
complement predictions made with the usual critical exponents, taken from data
in critical phenomena.


title: Nobility and Stupidity: Modeling the Evolution of Class Endogamy

abstract:
  Class endogamy is a phenomenon in which nobles only marry other nobles and
commoners only marry other commoners. The origin of class endogamy, and of
social stratification in general, is a major open question in archaeology. This
paper implements a verbal model proposed by Marcus and Flannery as a class of
agent-based computer models by generalizing and simplifying a mathematical
model of marriage markets developed by Burdett and Coles. One force that can
produce class endogamy occurs if agents are only willing to marry suitors
having status no less than some fixed value below the status of their
highest-status suitor, which they can learn. Another such force results if
children inherit the average of their parents' statuses. In contrast, status
achieved over an agent's lifetime can be viewed as noise, analogous to mutation
in biological evolution. I propose that class endogamy may have resulted from
the interaction of forces such as these, along with other factors such as
ideology. Simulation results are presented, and potential areas for future
research are sketched out. The validity of these models for any particular
culture depends, of course, on whether these forces were actually operating in
that society.


title: How Crucial is Small World Connectivity for Dynamics?

abstract:
  We study the dynamical behaviour of the collective field of chaotic systems
on small world lattices. Coupled neuronal systems as well as coupled logistic
maps are investigated. We observe that significant changes in dynamical
properties occur only at a reasonably high strength of nonlocal coupling.
Further, spectral features, such as signal-to-noise ratio (SNR), change
monotonically with respect to the fraction of random rewiring, i.e. there is no
optimal value of the rewiring fraction for which spectral properties are most
pronounced. We also observe that for small rewiring, results are similar to
those obtained by adding small noise.


title: Spatial Distributions of Observables in Systems under Thermal Gradients

abstract:
  Departures of observables from their thermal equilibrium expectation values
are studied under heat flow in steady-state non-equilibrium environments. The
relation between the spatial and temperature dependence of these
non-equilibrium behaviors and the underlying statistical properties are
clarified from general considerations. The predictions are then confirmed in
direct numerical simulations within the FPU-$\beta$ model. Non-equilibrium
momentum distribution functions are also examined and characterized through
their cumulants and the properties of higher order cumulants are discussed.


title:
Euler-Poincare formulation and elliptic instability for nth-gradient
  fluids

abstract:
  The energy of an $n^{th}-$gradient fluid depends on its Eulerian velocity
gradients of order $n$. A variational principle is introduced for the dynamics
of $n^{th}-$gradient fluids and their properties are reviewed in the context of
Noether's theorem. The stability properties of Craik-Criminale solutions for
first and second gradient fluids are examined.


title:
Estimation of a Noise Level Using Coarse-Grained Entropy of Experimental
  Time Series of Internal Pressure in a Combustion Engine

abstract:
  We report our results on non-periodic experimental time series of pressure in
a single cylinder spark ignition engine. The experiments were performed for
different levels of loading. We estimate the noise level in internal pressure
calculating the coarse-grained entropy from variations of maximal pressures in
successive cycles. The results show that the dynamics of the combustion is a
nonlinear multidimensional process mediated by noise. Our results show that so
defined level of noise in internal pressure is not monotonous function of
loading.


title: Dynamics of a Gear System with Faults in Meshing Stiffness

abstract:
  Gear box dynamics is characterised by a periodically changing stiffness. In
real gear systems, a backlash also exists that can lead to a loss in contact
between the teeth. Due to this loss of contact the gear has piecewise linear
stiffness characteristics, and the gears can vibrate regularly and chaotically.
In this paper we examine the effect of tooth shape imperfections and defects.
Using standard methods for nonlinear systems we examine the dynamics of gear
systems with various faults in meshing stiffness.


title:
A Numerical Study of a Simple Stochastic/Deterministic Model of
  Cycle-to-Cycle Combustion Fluctuations in Spark Ignition Engines

abstract:
  We examine a simple, fuel-air, model of combustion in a spark ignition (si)
engine with indirect injection. In our two fluid model, variations of fuel mass
burned in cycle sequences appear due to stochastic fluctuations of a fuel feed
amount. We have shown that a small amplitude of these fluctuations affects
considerably the stability of a combustion process strongly depending on the
quality of air-fuel mixture. The largest influence was found in the limit of a
lean combustion. The possible effect of nonlinearities in the combustion
process has been also discussed.


title: Exact solitary waves of the Korteveg - de Vries - Burgers equation

abstract:
  New approach is presented to search exact solutions of nonlinear differential
equations. This method is used to look for exact solutions of the Korteveg --
de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de
Vries -- Burgers equation are found.


title: Localised control for non-resonant Hamiltonian systems

abstract:
  We present a method of localised control of chaos in Hamiltonian systems. The
aim is to modify the perturbation locally by a small control term which makes
the controlled Hamiltonian more regular. We provide an explicit expression for
the control term which is able to recreate invariant (KAM) tori without
modifying other parts of phase space. We apply this method of localised control
to a forced pendulum model, to the delta-kicked rotor (standard map) and to a
non-twist Hamiltonian.


title: A mathematical description of natural shapes in our nonlinear world

abstract:
  The work presents two examples of simple mathematical formulas which are
natural nonlinear modifications (one being a generalization) of Gielis'
formula. These formulas involve a comparable number of parameters and provide
non-Platonic representations of a vast diversity of natural shapes and patterns
by incorporating diverse aspects of asymmetry and seeming disorder which are
absent in the original Gielis' formula. It is also shown how diverse sequences
resembling some natural-world pattern evolutions are also generated by such
nonlinear formulas.


title:
Correlations among the Riemann zeros: Invariance, resurgence, prophecy
  and self-duality

abstract:
  We present a conjecture describing new long range correlations among the
Riemann zeros leading to 3 principal features: (i) The spectral
auto-correlation is invariant w.r.t. the averaging window. (ii) Resurgence
occurs wherein the lowest zeros appear in all auto-correlations. (iii) Suitably
defined correlations lead to predictions (prophecy) of new zeros. This
conjecture is supported by analytical arguments and confirmed by numerical
calculations using 10^{22} zeros computed by Odlyzko. The results lead to a
self-duality of the Riemann spectrum similar to the quantum-classical duality
observed in billiards.


title: Stabilized vortex solitons in layered Kerr media

abstract:
  In this letter we demonstrate the possibility of stabilizing beams with
angular momentum propagating in Kerr media. Large propagation distances without
filamentation can be achieved in layered media with alternating focusing and
defocusing nonlinearities. Stronger stabilization can be obtained with the
addition of an incoherent beam.


title:
Weakly-nonlocal Symplectic Structures, Whitham method, and
  weakly-nonlocal Symplectic Structures of Hydrodynamic Type

abstract:
  We consider the special type of the field-theoretical Symplectic structures
called weakly nonlocal. The structures of this type are in particular very
common for the integrable systems like KdV or NLS. We introduce here the
special class of the weakly nonlocal Symplectic structures which we call the
weakly nonlocal Symplectic structures of Hydrodynamic Type. We investigate then
the connection of such structures with the Whitham averaging method and propose
the procedure of "averaging" of the weakly nonlocal Symplectic structures. The
averaging procedure gives the weakly nonlocal Symplectic Structure of
Hydrodynamic Type for the corresponding Whitham system. The procedure gives
also the "action variables" corresponding to the wave numbers of $m$-phase
solutions of initial system which give the additional conservation laws for the
Whitham system.


title:
Perturbing the topology of the Game of Life increases its robustness to
  asynchrony

abstract:
  An experimental analysis of the asynchronous version of the "Game of Life" is
performed to estimate how topology perturbations modify its evolution. We focus
on the study of a phase transition from an "inactive-sparse phase" to a
"labyrinth phase" and produce experimental data to quantify these changes as a
function of the density of the initial configuration, the value of the
synchrony rate, and the topology missing-link rate. An interpretation of the
experimental results is given using the hypothesis that initial "germs"
colonize the whole lattice and the validity of this hypothesis is tested.


title: A blue sky catastrophe in double-diffusive convection

abstract:
  A global bifurcation of the blue sky catastrophe type has been found in a
small Prandtl number binary mixture contained in a laterally heated cavity. The
system has been studied numerically applying the tools of bifurcation theory.
The catastrophe corresponds to the destruction of an orbit which, for a large
range of Rayleigh numbers, is the only stable solution. This orbit is born in a
global saddle-loop bifurcation and becomes chaotic in a period doubling cascade
just before its disappearance at the blue sky catastrophe.


title:
Direction Detector on an Excitable Field: Field Computation with
  Coincidence Detection

abstract:
  Living organisms process information without any central control unit and
without any ruling clock. We have been studying a novel computational strategy
that uses a geometrically arranged excitable field, i.e., "field computation."
As an extension of this research, in the present article we report the
construction of a "direction detector" on an excitable field. Using a numerical
simulation, we show that the direction of a input source signal can be detected
by applying the characteristic as a "coincidence detector" embedded on an
excitable field. In addition, we show that this direction detection actually
works in an experiment using an excitable chemical system. These results are
discussed in relation to the future development of "field computation."


title:
Subcritical modulational instability and transition to chaos from
  periodicity

abstract:
  This study shows that a modulationally destabilized monochromatic wave in a
fluid system may undergo a subcritical bifurcation directly into chaos, when
dissipation is weak enough. Analysis is made within the framework of the
complex Ginzburg-Landau equations.


title: Integrable Hamiltonian systems with vector potentials

abstract:
  We investigate integrable 2-dimensional Hamiltonian systems with scalar and
vector potentials, admitting second invariants which are linear or quadratic in
the momenta. In the case of a linear second invariant, we provide some examples
of weakly-integrable systems. In the case of a quadratic second invariant, we
recover the classical strongly-integrable systems in Cartesian and polar
coordinates and provide some new examples of integrable systems in parabolic
and elliptical coordinates.


title: Integrable quadratic Hamiltonians on so(4) and so(3,1)

abstract:
  We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1)
and describe Hamiltonians that have additional polynomial integrals. One of the
main results is a new integrable case with an integral of sixth degree.


title: Inversible Max-Plus Algebras and Integrable systems

abstract:
  We present an extended version of max-plus algebra which includes the inverse
operator of "max". This algebra enables us to ultra-discretize the system
including subtractions and obtain new ultra-discrete equations. The known
ultra-discrete equations can also be recovered by this construction.


title:
Phase shift analysis of PT-symmetric nonhermitian extension of A_{N-1}
  Calogero model without confining interaction

abstract:
  We discuss a many-particle quantum system, which is obtained by adding some
nonhermitian but PT (i.e. combined parity and time reversal) invariant
interaction to the $A_{N-1}$ rational Calogero model without confining
potential. This model gives rise to scattering states with continuous real
spectrum. The scattering phase shift is determined through the exchange
statistics parameter. We find that, unlike the case of usual Calogero model,
the exclusion and exchange statistics parameter differ from each other in the
presence of PT invariant interaction.


title: Group classification of nonlinear wave equations

abstract:
  We perform complete group classification of the general class of quasi linear
wave equations in two variables. This class may be seen as a broad
generalization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon and
Tzitzeica equations. In this way we derived a number of new genuinely nonlinear
invariant models with high symmetry properties. In particular, we obtain four
classes of nonlinear wave equations admitting five-dimensional invariance
groups. Applying the symmetry reduction technique we construct multi-parameter
families of exact solutions of those wave equations.


title: Models of Diffusive Noise on the Sphere

abstract:
  We analyze Haake et al. method for coarse graining quantum maps on the sphere
from the point of view of realizable physical quantum operations achieved with
completely positive superoperators. We conclude that sharp truncations a la
Haake do not fall into this class.


title: Possible Laws for Artificial Life Evolution

abstract:
  Motivated by a recent article on open problems in artificial life, here I
postulate three laws which form a mathematical framework to describe artificial
life evolutionary dynamics. They are based on a continuous approximation of
population dynamics. Four dynamical elements are required in this formulation:
ascendant matrix, transverse matrix, fitness function, and the stochastic
drive. The first law states that in the absence of stochastic drive the
artificial life always seeks for a local fitness attractor and stay there. It
gives the reference point to discuss the general evolutionary dynamics. The
second law is explicitly expressed in a unique form of stochastic differential
equation with all four dynamical elements. The third law defines the
relationship between the focused level of description to its lower and higher
ones, and also defines the dichotomy of deterministic and stochastic drives.
These laws provide a coherence framework to discuss several current problems,
such as emergency and stability. In particular, two quantities are emphasized:
the fitness function as the standard for selection and the stochasticity as the
source of creativity. Those three laws may appear almost self-evident from a
statistical physics point of view. However, their equivalent to a most
conventional approach for evolutionary dynamics is shown for the first time by
the present author, to the best of his knowledge. The computational advantage
of the present formulation in the study of artificial life evolution is also
discussed.


title: R-matrices and Spectrum of Vertex Models based on Superalgebras

abstract:
  In this paper we investigate trigonometric vertex models associated with
solutions of the Yang-Baxter equation which are invariant relative to
q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The
associated R-matrices are presented in terms of the standard Weyl basis making
possible the formulation of the quantum inverse scattering method for these
lattice models. This allowed us to derive the eigenvectors and the eigenvalues
of the corresponding transfer matrices as well as explicit expressions for the
Bethe ansatz equations.


title: Synchronization of two interacting populations of oscillators

abstract:
  We analyze synchronization between two interacting populations of different
phase oscillators. For the important case of asymmetric coupling functions, we
find a much richer dynamical behavior compared to that of symmetrically coupled
populations of identical oscillators (Okuda and Kuramoto, 1991). It includes
three types of bistabilities, higher order entrainment and the existence of
states with unusual stability properties. All possible routes to
synchronization of the populations are presented and some stability boundaries
are obtained analytically.


title: Lyapunov exponent for a gas of soft scatterers

abstract:
  For a fast particle moving within a two-dimensional array of soft scatterers
- centers of weak and short-range potential - the dependence of the Lyapunov
exponent on the system parameters is studied. The use of the linearized
equations for variations of the propagation angles and impact parameters of
consequent collisions reduces the problem to that of calculation of the
Lyapunov exponent of an ensemble of strongly correlated random matrices with
given statistics of matrix elements. In the simplest approximation this
Lyapunov exponent is proportional to the interaction strength and inversely
proportional to the square root of the interaction range. The model
satisfactorily describes the intensity of chaos in a system of two weakly
interacting particles moving in a two-dimensional regular confining potential.


title:
Time-dependent mode structure for Lyapunov vectors as a collective
  movement in quasi-one-dimensional systems

abstract:
  Time dependent mode structure for the Lyapunov vectors associated with the
stepwise structure of the Lyapunov spectra and its relation to the momentum
auto-correlation function are discussed in quasi-one-dimensional many-hard-disk
systems. We demonstrate mode structures (Lyapunov modes) for all components of
the Lyapunov vectors, which include the longitudinal and transverse components
of their spatial and momentum parts, and their phase relations are specified.
These mode structures are suggested from the form of the Lyapunov vectors
corresponding to the zero-Lyapunov exponents. Spatial node structures of these
modes are explained by the reflection properties of the hard-walls used in the
models. Our main interest is the time-oscillating behavior of Lyapunov modes.
It is shown that the largest time-oscillating period of the Lyapunov modes is
twice as long as the time-oscillating period of the longitudinal momentum
auto-correlation function. This relation is satisfied irrespective of the
particle number and boundary conditions. A simple explanation for this relation
is given based on the form of the Lyapunov vector.


title:
Simplest equation method to look for exact solutions of nonlinear
  differential equations

abstract:
  New method is presented to look for exact solutions of nonlinear differential
equations. Two basic ideas are at the heart of our approach. One of them is to
use the general solutions of the simplest nonlinear differential equations.
Another idea is to take into consideration all possible singularities of
equation studied. Application of our approach to search exact solutions of
nonlinear differential equations is discussed in detail. The method is used to
look for exact solutions of the Kuramoto - Sivashinsky equation and the
equation for description of nonlinear waves in a convective fluid. New exact
solitary and periodic waves of these equations are given.


title:
Pattern Formation in a Two-Dimensional Array of Oscillators with
  Phase-Shifted Coupling

abstract:
  We investigate the dynamics of a two-dimensional array of oscillators with
phase-shifted coupling. Each oscillator is allowed to interact with its
neighbors within a finite radius. The system exhibits various patterns
including squarelike pinwheels, (anti)spirals with phase-randomized cores, and
antiferro patterns embedded in (anti)spirals. We consider the symmetry
properties of the system to explain the observed behaviors, and estimate the
wavelengths of the patterns by linear analysis. Finally, we point out the
implications of our work for biological neural networks.


title:
A lattice Boltzmann study of non-hydrodynamic effects in shell models of
  turbulence

abstract:
  A lattice Boltzmann scheme simulating the dynamics of shell models of
turbulence is developed. The influence of high order kinetic modes (ghosts) on
the dissipative properties of turbulence dynamics is studied. It is
analytically found that when ghost fields relax on the same time scale as the
hydrodynamic ones, their major effect is a net enhancement of the fluid
viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve
on a much longer time scale. Analytical results are borne out by
high-resolution numerical simulations. These simulations indicate that the
hydrodynamic manifold is very robust towards large fluctuations of non
hydrodynamic fields.


title: Can two chaotic systems give rise to order?

abstract:
  The recently discovered Parrondo's paradox claims that two losing games can
result, under random or periodic alternation of their dynamics, in a winning
game: "losing+losing=winning". In this paper we follow Parrondo's philosophy of
combining different dynamics and we apply it to the case of one-dimensional
quadratic maps. We prove that the periodic mixing of two chaotic dynamics
originates an ordered dynamics in certain cases. This provides an explicit
example (theoretically and numerically tested) of a different Parrondian
paradoxical phenomenon: "chaos+chaos=order"


title: Universality in active chaos

abstract:
  Many examples of chemical and biological processes take place in large-scale
environmental flows. Such flows generate filamental patterns which are often
fractal due to the presence of chaos in the underlying advection dynamics. In
such processes, hydrodynamical stirring strongly couples into the reactivity of
the advected species and might thus make the traditional treatment of the
problem through partial differential equations difficult. Here we present a
simple approach for the activity in in-homogeneously stirred flows. We show
that the fractal patterns serving as skeletons and catalysts lead to a rate
equation with a universal form that is independent of the flow, of the particle
properties, and of the details of the active process. One aspect of the
universality of our appraoch is that it also applies to reactions among
particles of finite size (so-called inertial particles).


title: Pursuit-evasion predator-prey waves in two spatial dimensions

abstract:
  We consider a spatially distributed population dynamics model with excitable
predator-prey dynamics, where species propagate in space due to their taxis
with respect to each other's gradient in addition to, or instead of, their
diffusive spread. Earlier, we have described new phenomena in this model in one
spatial dimension, not found in analogous systems without taxis: reflecting and
self-splitting waves. Here we identify new phenomena in two spatial dimensions:
unusual patterns of meander of spirals, partial reflection of waves, swelling
wavetips, attachment of free wave ends to wave backs, and as a result, a novel
mechanism of self-supporting complicated spatio-temporal activity, unknown in
reaction-diffusion population models.


title:
Soliton-like phenomena in one-dimensional cross-diffusion systems: a
  predator-prey pursuit and evasion example

abstract:
  We have studied properties of nonlinear waves in a mathematical model of a
predator-prey system with pursuit and evasion. We demonstrate a new type of
propagating wave in this system. The mechanism of propagation of these waves
essentially depends on the ``taxis'', represented by nonlinear
``cross-diffusion'' terms in the mathematical formulation. We have shown that
the dependence of the velocity of wave propagation on the taxis has two
distinct forms, ``parabolic'' and ``linear''. Transition from one form to the
other correlates with changes in the shape of the wave profile. Dependence of
the propagation velocity on diffusion in this system differs from the
square-root dependence typical of reaction-diffusion waves. We demonstrate also
that, for systems with negative and positive taxis, for example, pursuit and
evasion, there typically exists a large region in the parameter space, where
the waves demonstrate quasisoliton interaction: colliding waves can penetrate
through each other, and waves can also reflect from impermeable boundaries.


title: Complexiton Solutions of the Toda Lattice Equation

abstract:
  A set of coupled conditions consisting of differential-difference equations
is presented for Casorati determinants to solve the Toda lattice equation. One
class of the resulting conditions leads to an approach for constructing
complexiton solutions to the Toda lattice equation through the Casoratian
formulation. An analysis is made for solving the resulting system of
differential-difference equations, thereby providing the general solution
yielding eigenfunctions required for forming complexitons. Moreover, a feasible
way is presented to compute the required eigenfunctions, along with examples of
real complexitons of lower order.


title: The overlapping of nonlinear resonances and problem of quantum chaos

abstract:
  The motion of a nonlinearly oscilating partical under the influence of a
periodic sequence of short impulses is investigated. We analyze the Schrodinger
equation for the universal Hamiltonian. The idea about the emerging of quantum
chaos due to the adiabatic motion along the curves of Mathieu characteristics
at multiple passages through the points of branching is advanced


title:
Self Running Droplet: Emergence of Regular Motion from Nonequilibrium
  Noise

abstract:
  Spontaneous motion of an oil droplet driven by chemical nonequilibricity is
reported. It is shown that the droplet undergoes regular rhythmic motion under
appropriately designed boundary conditions, whereas it exhibits random motion
in an isotropic environment. This study is a novel manifestation on the direct
energy transformation of chemical energy into regular spatial-motion under
isothermal conditions. A simple mathematical equation including noise
reproduces the essential feature of the transition from irregularity into
periodic regular motion. Our results will inspire the theoretical study on the
mechanism of molecular motors in living matter, working under significant
influence of thermal fluctuation.


title: On the Steklov-Lyapunov case of the rigid body motion

abstract:
  We construct a Poisson map between manifolds with linear Poisson brackets
corresponding to the two samples of Lie algebra $e(3)$. Using this map we
establish equivalence of the Steklov-Lyapunov system and the motion of a
particle on the surface of the sphere under the influence of the fourth order
potential. To study separation of variables for the Steklov case on the Lie
algebra $so(4)$ we use the twisted Poisson map between the bi-Hamiltonian
manifolds $e(3)$ and $so(4)$.


title:
The Quantum Double Pendulum: a Study of an Autonomous Classically
  Chaotic Quantum System

abstract:
  A numerical study of the quantum double pendulum is conducted. A suitable
quantum scaling is found which allows to have as the only parameters the ratios
of the lengths and masses of the two pendula and a (quantum) gravity parameter
containing Planck's constant. Comparison with classical and semiclassical
results is used to understand the behaviour of the energy curves of the levels,
to define regimes in terms of the gravity parameter, and to classify the
(resonant) interactions among levels by connecting them to various classical
phase space structures (resonance islands).


title:
Indirect Allee Effect, Bistability and Chaotic Oscillations in a
  Predator-Prey Discrete Model of Logistic Type

abstract:
  A cubic discrete coupled logistic equation is proposed to model the
predator-prey problem. The coupling depends on the population size of both
species and on a positive constant $\lambda$, which could depend on the prey
reproduction rate and on the predator hunting strategy. Different dynamical
regimes are obtained when $\lambda$ is modified. For small $\lambda$, the
species become extinct. For a bigger $\lambda$, the preys survive but the
predators extinguish. Only when the prey population reaches a critical value
then predators can coexist with preys. For increasing $\lambda$, a bistable
regime appears where the populations apart of being stabilized in fixed
quantities can present periodic, quasiperiodic and chaotic oscillations.
Finally, bistability is lost and the system settles down in a steady state, or,
for the biggest permitted $\lambda$, in an invariant curve. We also present the
basins for the different regimes. The use of the critical curves lets us
determine the influence of the zones with different number of first rank
preimages in the bifurcation mechanisms of those basins.


title:
Three Logistic Models for the Two-Species Interactions: Symbiosis,
  Predator-Prey and Competition

abstract:
  If one isolated species is supposed to evolve following the logistic mapping,
then we are tempted to think that the dynamics of two species can be expressed
by a coupled system of two discrete logistic equations. As three basic
relationships between two species are present in Nature, namely symbiosis,
predator-prey and competition, three different models are obtained. Each model
is a cubic two-dimensional discrete logistic-type equation with its own
dynamical properties: stationarity, periodicity, quasi-periodicity and chaos.
Furthermore, these models could be considered as the basic ingredients to
construct more complex interactions in the ecological networks.


title: Mixed integrable SU(N) vertex model with arbitrary twists

abstract:
  We consider the quantum inverse scattering method for several mixed
integrable models based on the rational SU(N) R-matrix with general toroidal
boundary conditions. This includes systems whose Hilbert spaces are invariant
by the discrete representations of the group SU(2) and the non-compact group
SU(1,1) as well as the conjugate representation of the SU(N) symmetry.
Introducing certain transformations on the quantum spaces we are able to solve
generalizaed impurity problems including those related to singular matrices.


title:
Smooth and Non-Smooth Dependence of Lyapunov Vectors upon the Angle
  Variable on a Torus in the Context of Torus-Doubling Transitions in the
  Quasiperiodically Forced Henon Map

abstract:
  A transition from a smooth torus to a chaotic attractor in quasiperiodically
forced dissipative systems may occur after a finite number of torus-doubling
bifurcations. In this paper we investigate the underlying bifurcational
mechanism which seems to be responsible for the termination of the
torus-doubling cascades on the routes to chaos in invertible maps under
external quasiperiodic forcing. We consider the structure of a vicinity of a
smooth attracting invariant curve (torus) in the quasiperiodically forced Henon
map and characterize it in terms of Lyapunov vectors, which determine
directions of contraction for an element of phase space in a vicinity of the
torus. When the dependence of the Lyapunov vectors upon the angle variable on
the torus is smooth, regular torus-doubling bifurcation takes place. On the
other hand, the onset of non-smooth dependence leads to a new phenomenon
terminating the torus-doubling bifurcation line in the parameter space with the
torus transforming directly into a strange nonchaotic attractor. We argue that
the new phenomenon plays a key role in mechanisms of transition to chaos in
quasiperiodically forced invertible dynamical systems.


title: Symmetry constraints for real dispersionless Veselov-Novikov equation

abstract:
  Symmetry constraints for dispersionless integrable equations are discussed.
It is shown that under symmetry constraints the dispersionless Veselov-Novikov
equation is reduced to the 1+1-dimensional hydrodynamic type systems.


title: Nonlinear absorption in discrete systems

abstract:
  In the context of nonlinear scattering, a continuous wave incident onto a
nonlinear discrete molecular chain of coupled oscillators can be partially
absorbed as a result of a 3-wave resonant interaction that couples two HF-waves
of frequencies close to the edge of the Brillouin zone. Hence both nonlinearity
and discreteness are necessary for generating this new absorption process which
manisfests itself by soliton generation in the medium. As a paradigm of this
nonlinear absorption we consider here the Davydov model that describes
exciton-phonon coupling in hydrogen bonded molecular chains.


title:
$sl(2|1)^{(2)}$ Gaudin Magnet and its associated Knizhnik-Zamolodchikov
  equation

abstract:
  The semiclassical limit of the algebraic Bethe Ansatz method is used to solve
the theory of Gaudin models for the $sl(2|1)^{(2)}$ R-matrix. We find the
spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also
use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation
solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.


title: Reductions of the Volterra lattice

abstract:
  We exhibit three classes of algebraic constraints which are shown compatible
with Volterra lattice.


title:
Estimation of System Parameters and Predicting the Flow Function from
  Time Series of Continuous Dynamical Systems

abstract:
  We introduce a simple method to estimate the system parameters in continuous
dynamical systems from the time series. In this method, we construct a modified
system by introducing some constants (controlling constants) into the given
(original) system. Then the system parameters and the controlling constants are
determined by solving a set of nonlinear simultaneous algebraic equations
obtained from the relation connecting original and modified systems. Finally,
the method is extended to find the form of the evolution equation of the system
itself. The major advantage of the method is that it needs only a minimal
number of time series data and is applicable to dynamical systems of any
dimension. The method also works extremely well even in the presence of noise
in the time series. This method is illustrated for the case of Lorenz system.


title: Multi-field continuum theory for medium with microscopic rotations

abstract:
  We derive the multi-field, micropolar-type continuum theory for the
two-dimensional model of crystal having finite-size particles. Continuum
theories are usually valid for waves with wavelength much larger than the size
of primitive cell of crystal. By comparison of the dispersion relations, it is
demonstrated that in contrast to the single-field continuum theory constructed
in our previous paper the multi-field generalization is valid not only for long
but also for short waves. We show that the multi-field model can be used to
describe spatially localized short- and long wavelength distortions. Short-wave
external fields of forces and torques can be also naturally taken into account
by the multi-field continuum theory.


title: Lagrangian Formalism in Perturbed Nonlinear Klein-Gordon Equations

abstract:
  We develop an alternative approach to study the effect of the generic
perturbation (in addition to explicitly considering the loss term) in the
nonlinear Klein-Gordon equations. By a change of the variables that cancel the
dissipation term we are able to write the Lagrangian density and then,
calculate the Lagrangian as a function of collective variables. We use the
Lagrangian formalism together with the Rice {\it Ansatz} to derive the
equations of motion of the collective coordinates (CCs) for the perturbed
sine-Gordon (sG) and $\phi^{4}$ systems. For the $N$ collective coordinates,
regardless of the {\it Ansatz} used, we show that, for the nonlinear
Klein-Gordon equations, this approach is equivalent to the {\it Generalized
Traveling Wave Ansatz} ({\it GTWA})


title: Synchronization regimes in systems with multiple time-delays

abstract:
  We present the first report on chaos synchronization between two
unidirectionally linearly and nonlinearly coupled systems with multiple
time-delays and using the Razumikhin-Lyapunov approach find the existence and
stability conditions for different synchronization regimes.The approach is
tested on the famous nonlinear models-Ikeda, Mackey-Glass, and Lang-Kobayashi
systems.


title:
Inherent Frequency and Spatial Decomposition of the Lorenz Chaotic
  Attractor

abstract:
  This letter suggests a new way to investigate 3-D chaos in spatial and
frequency domains simultaneously. After spatially decomposing the Lorenz
attractor into two separate scrolls with peaked spectra and a 1-D discrete-time
zero-crossing series with a wide-band spectrum, it is found that the Lorenz
chaotic attractor has an inherent frequency uniquely determined by the three
system parameters. This result implies that chaos in the Lorenz attractor is
mainly exhibited when the trajectory crosses from one scroll to another, not
within the two scrolls. This is also true for some other double-scroll
Lorenz-like chaotic attractors, such as Chua's attractor. Some possible
applications of the inherent frequency and the spatial decomposition are also
discussed.


title: A strange recursion operator demystified

abstract:
  We show that a new integrable two-component system of KdV type studied by
Karasu (Kalkanli) et al. (arXiv: nlin.SI/0203036) is bihamiltonian, and its
recursion operator, which has a highly unusual structure of nonlocal terms, can
be written as a ratio of two compatible Hamiltonian operators.
  Using this, we prove that the system in question possesses an infinite
hierarchy of local commuting generalized symmetries and conserved quantities in
involution, and the evolution systems corresponding to these symmetries are
bihamiltonian as well.
  We also show that upon introduction of suitable nonlocal variables the
nonlocal terms of the recursion operator under study can be written in the
usual form, with the integration operator $D^{-1}$ appearing in each term at
most once.


title: Young diagrams and N-soliton solutions of the KP equation

abstract:
  We consider $N$-soliton solutions of the KP equation,
(-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An $N$-soliton solution is a solution
$u(x,y,t)$ which has the same set of $N$ line soliton solutions in both
asymptotics $y\to\infty$ and $y\to -\infty$. The $N$-soliton solutions include
all possible resonant interactions among those line solitons. We then classify
those $N$-soliton solutions by defining a pair of $N$-numbers $({\bf n}^+,{\bf
n}^-)$ with ${\bf n}^{\pm}=(n_1^{\pm},...,n_N^{\pm}),
n_j^{\pm}\in\{1,...,2N\}$, which labels $N$ line solitons in the solution. The
classification is related to the Schubert decomposition of the Grassmann
manifolds Gr$(N,2N)$, where the solution of the KP equation is defined as a
torus orbit. Then the interaction pattern of $N$-soliton solution can be
described by the pair of Young diagrams associated with $({\bf n}^+,{\bf
n}^-)$. We also show that $N$-soliton solutions of the KdV equation obtained by
the constraint $\partial u/\partial y=0$ cannot have resonant interaction.


title: Multi-frequency control of Faraday wave patterns

abstract:
  We show how pattern formation in Faraday waves may be manipulated by varying
the harmonic content of the periodic forcing function. Our approach relies on
the crucial influence of resonant triad interactions coupling pairs of critical
standing wave modes with damped, spatio-temporally resonant modes. Under the
assumption of weak damping and forcing, we perform a symmetry-based analysis
that reveals the damped modes most relevant for pattern selection, and how the
strength of the corresponding triad interactions depends on the forcing
frequencies, amplitudes, and phases. In many cases, the further assumption of
Hamiltonian structure in the inviscid limit determines whether the given triad
interaction has an enhancing or suppressing effect on related patterns.
Surprisingly, even for forcing functions with arbitrarily many frequency
components, there are at most five frequencies that affect each of the
important triad interactions at leading order. The relative phases of those
forcing components play a key role, sometimes making the difference between an
enhancing and suppressing effect. In numerical examples, we examine the
validity of our results for larger values of the damping and forcing. Finally,
we apply our findings to one-dimensional periodic patterns obtained with
impulsive forcing and to two-dimensional superlattice patterns and
quasipatterns obtained with multi-frequency forcing.


title:
Generating Function Associated with the Determinant Formula for the
  Solutions of the Painleve' II Equation

abstract:
  In this paper we consider a Hankel determinant formula for generic solutions
of the Painleve' II equation. We show that the generating functions for the
entries of the Hankel determinants are related to the asymptotic solution at
infinity of the linear problem of which the Painleve' II equation describes the
isomonodromic deformations.


title:
Methods of geometry of differential equations in analysis of the
  integrable field theory models

abstract:
  In this paper, we investigate the algebraic and geometric properties of the
hyperbolic Toda equations $u_{xy}=\exp(Ku)$ associated with nondegenerate
symmetrizable matrices $K$. A hierarchy of analogs to the potential modified
Korteweg-de Vries equation $u_t=u_{xxx}+u_x^3$ is constructed, and its relation
with the hierarchy for the Korteweg-de Vries equation $T_t=T_{xxx}+TT_x$ is
established. Group-theoretic structures for the dispersionless
(2+1)-dimensional Toda equation $u_{xy}=\exp(-u_{zz})$ are obtained. Geometric
properties of the multi-component nonlinear Schr\"odinger equation type systems
$\Psi_t = i\Psi_{xx} + i f(|\Psi|) \Psi$ (multi-soliton complexes) are
described.


title: Towards a dynamical theory of multifractals in turbulence

abstract:
  Making use of the exact equations for structure functions, supplemented by
the equations for dissipa tive anomaly as well as an estimate for the
Lagrangian acceleration of fluid particles, we obtain a main result of the
multifractal theory of turbulence. The central element of the theory is a
dissipation cut-off that depends on the order of the structure function. An
expression obtained for the exponents $s_{n}$ in the scaling relations
$\bar{(\frac{\partial u}{\partial x})^{n}}/\bar{(\frac{\partial u}{\partial
x})^{2}}^{\frac{n}{2}} \propto Re^{s_{n}}$, between the velocity gradients
$\frac{\partial u}{\partial x}$ and the Reynolds number $Re$, agrees well with
experimental data.


title:
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions
  of Painlev\'e VI

abstract:
  Equivalence is established between a special class of Painleve VI equations
parametrized by a conformal dimension $\mu$, time dependent Euler top
equations, isomonodromic deformations and three-dimensional Frobenius
manifolds. The isomodromic tau function and solutions of the Euler top
equations are explicitly constructed in terms of Wronskian solutions of the
2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by
means of Grassmannian formulation. These Wronskian solutions give rational
solutions of the Painleve VI equation for $\mu=1,2,{...} $.


title:
Estimating short-time period to break different types of chaotic
  modulation based secure communications

abstract:
  In recent years, chaotic attractors have been extensively used in the design
of secure communication systems. One of the preferred ways of transmitting the
information signal is binary chaotic modulation, in which a binary message
modulates a parameter of the chaotic generator. This paper presents a method of
attack based on estimating the short-time period of the ciphertext generated
from the modulated chaotic attractor. By calculating and then filtering the
short-time period of the transmitted signal it is possible to obtain the binary
information signal with great accuracy without any knowledge of the parameters
of the underlying chaotic system. This method is successfully applied to
various secure communication systems proposed in the literature based on
different chaotic attractors.


title: Quantum discrete Dubrovin equations

abstract:
  The discrete equations of motion for the quantum mappings of KdV type are
given in terms of the Sklyanin variables (which are also known as quantum
separated variables). Both temporal (discrete-time) evolutions and spatial
(along the lattice at a constant time-level) evolutions are considered. In the
classical limit, the temporal equations reduce to the (classical) discrete
Dubrovin equations as given in a previous publication. The reconstruction of
the original dynamical variables in terms of the Sklyanin variables is also
achieved.


title: Incoherent vector vortex-mode solitons in self-focusing nonlinear media

abstract:
  We suggest a novel type of composite spatial optical soliton created by a
coherent vortex beam guiding a partially incoherent light beam in a
self-focusing nonlinear medium. We show that the incoherence of the guided mode
may enhance, rather than suppress, the vortex azimuthal instability, and also
demonstrate strong destabilization of dipole-mode solitons by partially
incoherent light.


title: Periodic orbit spectrum in terms of Ruelle--Pollicott resonances

abstract:
  Fully chaotic Hamiltonian systems possess an infinite number of classical
solutions which are periodic, e.g. a trajectory ``p'' returns to its initial
conditions after some fixed time tau_p. Our aim is to investigate the spectrum
tau_1, tau_2, ... of periods of the periodic orbits. An explicit formula for
the density rho(tau) = sum_p delta (tau - tau_p) is derived in terms of the
eigenvalues of the classical evolution operator. The density is naturally
decomposed into a smooth part plus an interferent sum over oscillatory terms.
The frequencies of the oscillatory terms are given by the imaginary part of the
complex eigenvalues (Ruelle--Pollicott resonances). For large periods,
corrections to the well--known exponential growth of the smooth part of the
density are obtained. An alternative formula for rho(tau) in terms of the zeros
and poles of the Ruelle zeta function is also discussed. The results are
illustrated with the geodesic motion in billiards of constant negative
curvature. Connections with the statistical properties of the corresponding
quantum eigenvalues, random matrix theory and discrete maps are also
considered. In particular, a random matrix conjecture is proposed for the
eigenvalues of the classical evolution operator of chaotic billiards.


title: Spectral Analysis and the Dynamic Response of Complex Networks

abstract:
  The eigenvalues and eigenvectors of the connectivity matrix of complex
networks contain information about its topology and its collective behavior. In
particular, the spectral density $\rho(\lambda)$ of this matrix reveals
important network characteristics: random networks follow Wigner's semicircular
law whereas scale-free networks exhibit a triangular distribution. In this
paper we show that the spectral density of hierarchical networks follow a very
different pattern, which can be used as a fingerprint of modularity. Of
particular importance is the value $\rho(0)$, related to the homeostatic
response of the network: it is maximum for random and scale free networks but
very small for hierarchical modular networks. It is also large for an actual
biological protein-protein interaction network, demonstrating that the current
leading model for such networks is not adequate.


title: A New Nonextensive Entropy

abstract:
  We propose a new way of defining entropy of a system, which gives a general
form which may be nonextensive as Tsallis entropy, but is linearly dependent on
component entropies, like Renyi entropy, which is extensive. This entropy has a
conceptually novel but simple origin and is mathematically easy to define by a
very simple expression, though the probability distribution resulting from
optimizing it gives rather complex, which is compared numerically with the
other entropies. It may, therefore, appear as the right candidate in a physical
situation where the probability distribution does not suit any of the
previously defined forms.


title:
Localised and nonlocalised structures in nonlinear lattices with
  fermions

abstract:
  We discuss the quasiclassical approximation for the equations of motions of a
nonlinear chain of phonons and electrons having phonon mediated hopping.
Describing the phonons and electrons as even and odd grassmannian functions and
using the continuum limit we show that the equations of motions lead to a
Zakharov-like system for bosonic and fermionic fields. Localised and
nonlocalised solutions are discussed using the Hirota bilinear formalism.
Nonlocalised solutions turn out to appear naturally for any choice of wave
parameters. The bosonic localised solution has a fermionic dressing while the
fermionic one is an oscillatory localised field. They appear only if some
constraints on the dispersion are imposed. In this case the density of fermions
is a strongly localised travelling wave. Also it is shown that in the multiple
scales approach the emergent equation is linear. Only for the resonant case we
get a nonlinear fermionic Yajima-Oikawa system. Physical implications are
discussed.


title:
Terminating ventricular tachycardia by pacing induced dynamical
  inhomogeneities in the reentry circuit

abstract:
  Formation of feedback loops of excitation waves (reentrant circuit) around
non-conducting ventricular scar tissue is a common cause of lethal cardiac
arrhythmias, such as ventricular tachycardia. This is typically treated by
rapid stimulation from an implantable device (ICD). However, the mechanisms of
reentry termination success and, more importantly, failure, are poorly
understood. To study such mechanisms, we simulated pacing of anatomical reentry
in an ionic model of cardiac tissue, having significant restitution and
dispersion properties. Our results show that rapid pacing causes inhomogeneous
conduction in the reentrant circuit, leading to successful pacing termination
of tachycardia. The study suggests that more effective pacing algorithms can be
designed by taking into account the role of such dynamical inhomogeneities.


title:
Controlling spatiotemporal chaos in excitable media by local biphasic
  stimulation

abstract:
  Controlling spatiotemporal chaos in excitable media by applying low-amplitude
perturbations {\em locally} is of immediate applicability, e.g., in treating
ventricular fibrillation, a fatal disturbance in the normal rhythmic
functioning of the heart. We look at a mechanism of control by the local
application of a series of biphasic pulses, i.e., involving both positive and
negative stimulation. This results in faster recovery of the medium, making it
possible to overdrive the chaos by generating waves with frequency higher than
that possible with only positive pulses. This provides the simplest and most
general understanding of the effectiveness of biphasic stimulation in
controlling fibrillation and allows designing optimal waveshapes for
controlling spatiotemporal chaos.


title: Spiraling of adjacent trajectories in chaotic systems

abstract:
  The spiraling of adjacent trajectories in chaotic dynamical systems can be
characterized by distribution of local angular velocities of rotation of the
displacement vector, which is governed by linearized equations of motion. This
distribution, akin to that of local Lyapunov exponents, is studied for three
examples of three-dimensional flows. Toy model shows that the rotation rate of
adjacent trajectories influences on the rate of mixing of dynamic variables and
on the sensitivity of trajectories to perturbations.


title:
Is Multiscaling an Artifact in the Stochastically Forced Burgers
  Equation?

abstract:
  We study turbulence in the one-dimensional Burgers equation with a
white-in-time, Gaussian random force that has a Fourier-space spectrum $\sim
1/k$, where $k$ is the wave number. From very-high-resolution numerical
simulations, in the limit of vanishing viscosity, we find evidence for
multiscaling of velocity structure functions which cannot be falsified by
standard tests. We find a new artifact in which logarithmic corrections can
appear disguised as anomalous scaling and conclude that bifractal scaling is
likely.


title:
Algebraic Bethe Ansatz for the Zamolodchikov-Fateev and Izergin-Korepin
  models with open boundary conditions

abstract:
  We have considered the Zamolodchikov-Fateev and the Izergin-Korepin models
with diagonal reflection boundaries. In each case the eigenspectrum of the
transfer matrix is determined by application of the algebraic Bethe Ansatz.


title:
Spiral modes in the diffusion of a granular particle on a vibrating
  surface

abstract:
  We consider a particle that is subject to a constant force and scatters
inelastically on a vibrating periodically corrugated floor. At small friction
and small radius of the circular scatterers the dynamics is dominated by
resonances forming spiral structures in phase space. These spiral modes lead to
pronounced maxima and minima in the diffusion coefficient as a function of the
vibration frequency, as is shown in computer simulations. Our theoretical
predictions may be verified experimentally by studying transport of granular
matter on vibratory conveyors.


title:
Stabilization of a light bullet in a layered Kerr medium with
  sign-changing nonlinearity

abstract:
  Using the numerical solution of the nonlinear Schr\"odinger equation and a
variational method it is shown that (3+1)-dimensional spatiotemporal optical
solitons, known as light bullets, can be stabilized in a layered Kerr medium
with sign-changing nonlinearity along the propagation direction.


title: Awaking and Sleeping a Complex Network

abstract:
  A network with local dynamics of logistic type is considered. We implement a
mean-field multiplicative coupling among first-neighbor nodes. When the
coupling parameter is small the dynamics is dissipated and there is no
activity: the network is {\it turned off}. For a critical value of the coupling
a non-null stable synchronized state, which represents a {\it turned on}
network, emerges. This global bifurcation is independent of the network
topology. We characterize the bistability of the system by studying how to
perform the transition, which now is topology dependent, from the active state
to that with no activity, for the particular case of a scale free network. This
could be a naive model for the {\it wakening} and {\it sleeping} of a
brain-like system.

categories: nlin.AO cond-mat.dis-nn nlin.PS q-bio.NC


title: Semiclassical Accuracy in Phase Space for Regular and Chaotic Dynamics

abstract:
  A phase-space semiclassical approximation valid to $O(\hbar)$ at short times
is used to compare semiclassical accuracy for long-time and stationary
observables in chaotic, stable, and mixed systems. Given the same level of
semiclassical accuracy for the short time behavior, the squared semiclassical
error in the chaotic system grows linearly in time, in contrast with quadratic
growth in the classically stable system. In the chaotic system, the relative
squared error at the Heisenberg time scales linearly with $\hbar_{\rm eff}$,
allowing for unambiguous semiclassical determination of the eigenvalues and
wave functions in the high-energy limit, while in the stable case the
eigenvalue error always remains of the order of a mean level spacing. For a
mixed classical phase space, eigenvalues associated with the chaotic sea can be
semiclassically computed with greater accuracy than the ones associated with
stable islands.


title:
Semi-classical analysis of real atomic spectra beyond Gutzwiller's
  approximation

abstract:
  Real atomic systems, like the hydrogen atom in a magnetic field or the helium
atom, whose classical dynamics are chaotic, generally present both discrete and
continuous symmetries. In this letter, we explain how these properties must be
taken into account in order to obtain the proper (i.e. symmetry projected)
$\hbar$ expansion of semiclassical expressions like the Gutzwiller trace
formula. In the case of the hydrogen atom in a magnetic field, we shed light on
the excellent agreement between present theory and exact quantum results.


title: The Fermi-Ulam Accelerator Model Under Scaling Analysis

abstract:
  The chaotic low energy region of the Fermi-Ulam simplified accelerator model
is characterised by use of scaling analysis. It is shown that the average
velocity and the roughness (variance of the average velocity) obey scaling
functions with the same characteristic exponents. The formalism is widely
applicable, including to billiards and to other chaotic systems.


title: Democracy: Order out of Chaos

abstract:
  We construct a majority cellular automata based model to explain the
power-law signatures in Indonesian general election results. The understanding
of second-order phase transitions between two different conditions inspires the
model. The democracy is assumed as critical point between the two extreme
socio-political situations of totalitarian and anarchistic social system -
where democracy can fall into the twos. The model is in multi-party candidates
system run for equilibrium or equilibria, and used to fit and analyze the three
of democratic national elections in Indonesia, 1955, 1999, and 2004.


title:
Objects That Make Objects: The Population Dynamics of Structural
  Complexity

abstract:
  To analyze the evolutionary emergence of structural complexity in physical
processes we introduce a general, but tractable, model of objects that interact
to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well
defined structural properties, we demonstrate that complexity in the resulting
population dynamical system emerges on several distinct organizational scales
during evolution--from individuals to nested levels of mutually self-sustaining
interaction. The evolution to increased organization is dominated by the
spontaneous creation of structural hierarchies and this, in turn, is
facilitated by the innovation and maintenance of relatively low-complexity, but
general individuals.


title:
Resonance and web structure in discrete soliton systems: the
  two-dimensional Toda lattice and its fully discrete and ultra-discrete
  versions

abstract:
  We present a class of solutions of the two-dimensional Toda lattice equation,
its fully discrete analogue and its ultra-discrete limit. These solutions
demonstrate the existence of soliton resonance and web-like structure in
discrete integrable systems such as differential-difference equations,
difference equations and cellular automata (ultra-discrete equations).


title:
Simulated Dynamical Weakening and Abelian Avalanches in Mean-Field
  Driven Threshold Models

abstract:
  Mean-field coupled lattice maps are used to approximate the physics of driven
threshold systems with long range interactions. However, they are incapable of
modeling specific features of the dynamic instability responsible for
generating avalanches. Here we present a method of simulating specific
frictional weakening effects in a mean field slider block model. This provides
a means of exploring dynamical effects previously inaccessible to discrete time
simulations. This formulation also results in Abelian avalanches, where rupture
propagation is independent of the failure sequence. The resulting event size
distribution is shown to be generated by the boundary crossings of a stochastic
process. This is applied to typical models to explain some commonly observed
features.


title:
Drag Reduction by Microbubbles in Turbulent Flows: the Limit of Minute
  Bubbles

abstract:
  Drag reduction by microbubbles is a promising engineering method for
improving ship performance. A fundamental theory of the phenomenon is lacking
however, making actual design quite uphazard. We offer here a theory of drag
reduction by microbubbles in the limit of very small bubbles, when the effect
of the bubbles is mainly to normalize the density and the viscosity of the
carrier fluid. The theory culminates with a prediction of the degree of drag
reduction given the concentration profile of the bubbles. Comparisons with
experiments are discussed and the road ahead is sketched.


title:
Noise Induced Dissipation in Discrete-Time Classical and Quantum
  Dynamical Systems

abstract:
  We introduce a new characteristics of chaoticity of classical and quantum
dynamical systems by defining the notion of the dissipation time which enables
us to test how the system responds to the noise and in particular to measure
the speed at which an initially closed, conservative system converges to the
equilibrium when subjected to noisy (stochastic) perturbations. We prove fast
dissipation result for classical Anosov systems and general exponentially
mixing maps. Slow dissipation result is proved for regular systems including
non-weakly mixing maps. In quantum setting we study simultaneous semiclassical
and small noise asymptotics of the dissipation time of quantized toral
symplectomorphisms (generalized cat maps) and derive sharp bounds for
semiclassical regime in which quantum-classical correspondence of dissipation
times holds.


title: Bose-Einstein Condensates in Superlattices

abstract:
  We consider the Gross-Pitaevskii (GP) equation in the presence of periodic
and quasiperiodic superlattices to study cigar-shaped Bose-Einstein condensates
(BECs) in such potentials. We examine spatially extended wavefunctions in the
form of modulated amplitude waves (MAWs). With a coherent structure ansatz, we
derive amplitude equations describing the evolution of spatially modulated
states of the BEC. We then apply second-order multiple scale perturbation
theory to study harmonic resonances with respect to a single lattice wavenumber
as well as ultrasubharmonic resonances that result from interactions of both
wavenumbers of the superlattice. In each case, we determine the resulting
system's equilibria, which represent spatially periodic solutions, and
subsequently examine the stability of the corresponding solutions by direct
simulations of the GP equation, identifying them as typically stable solutions
of the model. We then study subharmonic resonances using Hamiltonian
perturbation theory, tracing robust, spatio-temporally periodic patterns.

categories: nlin.PS cond-mat.soft nlin.CD physics.atom-ph


title:
Robustness of the noise-induced phase synchronization in a general class
  of limit cycle oscillators

abstract:
  We show that a wide class of uncoupled limit cycle oscillators can be
in-phase synchronized by common weak additive noise. An expression of the
Lyapunov exponent is analytically derived to study the stability of the
noise-driven synchronizing state. The result shows that such a synchronization
can be achieved in a broad class of oscillators with little constraint on their
intrinsic property. On the other hand, the leaky integrate-and-fire neuron
oscillators do not belong to this class, generating intermittent phase slips
according to a power low distribution of their intervals.


title:
Cryptanalyzing an improved security modulated chaotic encryption scheme
  using ciphertext absolute value

abstract:
  This paper describes the security weakness of a recently proposed improved
chaotic encryption method based on the modulation of a signal generated by a
chaotic system with an appropriately chosen scalar signal. The aim of the
improvement is to avoid the breaking of chaotic encryption schemes by means of
the return map attack introduced by Perez and Cerdeira. A method of attack
based on taking the absolute value of the ciphertext is presented, that allows
for the cancellation of the modulation scalar signal and the determination of
some system parameters that play the role of system key. The proposed improved
method is shown to be compromised without any knowledge of the chaotic system
parameter values and even without knowing the transmitter structure.