title:
Factorization of the transfer matrices for the quantum sl(2) spin chains
  and Baxter equation

abstract:
  It is shown that the transfer matrices of homogeneous sl(2) invariant spin
chains with generic spin, both closed and open, are factorized into the product
of two operators. The latter satisfy the Baxter equation that follows from the
structure of the reducible representations of the sl(2) algebra.


title:
Modeling Endogenous Social Networks: the Example of Emergence and
  Stability of Cooperation without Refusal

abstract:
  Aggregated phenomena in social sciences and economics are highly dependent on
the way individuals interact. To help understanding the interplay between
socio-economic activities and underlying social networks, this paper studies a
sequential prisoner's dilemma with binary choice. It proposes an analytical and
computational insight about the role of endogenous networks in emergence and
sustainability of cooperation and exhibits an alternative to the choice and
refusal mechanism that is often proposed to explain cooperation. The study
focuses on heterogeneous equilibriums and emergence of cooperation from an
all-defector state that are the two stylized facts that this model successfully
reconstructs.

categories: nlin.AO cond-mat.other cs.GT cs.MA cs.OH q-bio.OT q-bio.PE


title: Finite amplitude waves under a small resonant driving force

abstract:
  We construct a special asymptotic solution for the forced Boussinesq
equation. The perturbation is small and oscillates with a slowly varied
frequency. The slow passage through the resonance generates waves with the
finite amplitude. This phenomenon is described in details.


title: Dynamic Critical approach to Self-Organized Criticality

abstract:
  A dynamic scaling Ansatz for the approach to the Self-Organized Critical
(SOC) regime is proposed and tested by means of extensive simulations applied
to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering
the short-time scaling behavior of the density of sites ($\rho(t)$) below the
critical value, it is shown that i) starting the dynamics with configurations
such that $\rho(t=0) \to 0$ one observes an {\it initial increase} of the
density with exponent $\theta = 0.12(2)$; ii) using initial configurations with
$\rho(t=0) \to 1$, the density decays with exponent $\delta = 0.47(2)$. It is
also shown that he temporal autocorrelation decays with exponent $C_a =
0.35(2)$. Using these, dynamically determined, critical exponents and suitable
scaling relationships, all known exponents of the BS model can be obtained,
e.g. the dynamical exponent $z = 2.10(5)$, the mass dimension exponent $D =
2.42(5)$, and the exponent of all returns of the activity $\tau_{ALL} =
0.39(2)$, in excellent agreement with values already accepted and obtained
within the SOC regime.


title:
Bi-Hamiltonian operators, integrable flows of curves using moving
  frames, and geometric map equations

abstract:
  Moving frames of various kinds are used to derive bi-Hamiltonian operators
and associated hierarchies of multi-component soliton equations from
group-invariant flows of non-stretching curves in constant curvature manifolds
and Lie group manifolds. The hierarchy in the constant-curvature case consists
of a vector mKdV equation coming from a parallel frame, a vector potential mKdV
equation coming from a covariantly-constant frame, and higher order
counterparts generated by an underlying vector mKdV recursion operator. In the
Lie-group case the hierarchy comprises a group-invariant analog of the vector
NLS equation coming from a left-invariant frame, along with higher order
counterparts generated by a recursion operator that is like a square-root of
the mKdV one. The corresponding respective curve flows are found to be given by
geometric nonlinear PDEs, specifically mKdV and group-invariant analogs of
Schrodinger maps. In all cases the hierarchies also contain variants of vector
sine-Gordon equations arising from the kernel of the respective recursion
operators. The geometric PDEs that describe the corresponding curve flows are
shown to be wave maps. Full details of these results are presented for two main
cases: $S^2,S^3\simeq SU(2)$.


title:
Multistable Solitons in the Cubic-Quintic Discrete Nonlinear
  Schr\"odinger Equation

abstract:
  We analyze the existence and stability of localized solutions in the
one-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation with a
combination of competing self-focusing cubic and defocusing quintic onsite
nonlinearities. We produce a stability diagram for different families of
soliton solutions, that suggests the (co)existence of infinitely many branches
of stable localized solutions. Bifurcations which occur with the increase of
the coupling constant are studied in a numerical form. A variational
approximation is developed for accurate prediction of the most fundamental and
next-order solitons together with their bifurcations. Salient properties of the
model, which distinguish it from the well-known cubic DNLS equation, are the
existence of two different types of symmetric solitons and stable asymmetric
soliton solutions that are found in narrow regions of the parameter space. The
asymmetric solutions appear from and disappear back into the symmetric ones via
loops of forward and backward pitchfork bifurcations.


title: Stable rotating dipole solitons in nonlocal optical media

abstract:
  We reveal that nonlocality can provide a simple physical mechanism for
stabilization of multi-hump optical solitons, and present the first example of
stable rotating dipole solitons and soliton spiraling, known to be unstable in
all types of realistic nonlinear media with local response.


title: On Classical r-Matrix for the Kowalevski Gyrostat on so(4)

abstract:
  We present the trigonometric Lax matrix and classical r-matrix for the
Kowalevski gyrostat on so(4) algebra by using the auxiliary matrix algebras
so(3,2) or sp(4).


title: Complexity and Non-Commutativity of Learning Operations on Graphs

abstract:
  We present results from numerical studies of supervised learning operations
in recurrent networks considered as graphs, leading from a given set of input
conditions to predetermined outputs. Graphs that have optimized their output
for particular inputs with respect to predetermined outputs are asymptotically
stable and can be characterized by attractors which form a representation space
for an associative multiplicative structure of input operations. As the mapping
from a series of inputs onto a series of such attractors generally depends on
the sequence of inputs, this structure is generally non-commutative. Moreover,
the size of the set of attractors, indicating the complexity of learning, is
found to behave non-monotonically as learning proceeds. A tentative relation
between this complexity and the notion of pragmatic information is indicated.


title: Breather-like pulses in a medium with the permanent dipole moment

abstract:
  The solutions of the reduced Maxwell-Bloch equations for an anisotropic
two-level medium, which describe the propagation of electromagnetic pulses
having a duration from a few field oscillations, are studied. An influence of
the permanent dipole moment of the quantum transition on dynamics of the pulses
and their spectrum is considered.


title: Theory of small aspect ratio waves in deep water

abstract:
  In the limit of small values of the aspect ratio parameter (or wave
steepness) which measures the amplitude of a surface wave in units of its
wave-length, a model equation is derived from the Euler system in infinite
depth (deep water) without potential flow assumption. The resulting equation is
shown to sustain periodic waves which on the one side tend to the proper linear
limit at small amplitudes, on the other side possess a threshold amplitude
where wave crest peaking is achieved. An explicit expression of the crest angle
at wave breaking is found in terms of the wave velocity. By numerical
simulations, stable soliton-like solutions (experiencing elastic interactions)
propagate in a given velocities range on the edge of which they tend to the
peakon solution.


title: Periodic-Orbit Approach to Universality in Quantum Chaos

abstract:
  We show that in the semiclassical limit, classically chaotic systems have
universal spectral statistics. Concentrating on short-time statistics, we
identify the pairs of classical periodic orbits determining the small-$\tau$
behavior of the spectral form factor $K(\tau)$ of fully chaotic systems. The
two orbits within each pair differ only by their connections inside close
self-encounters in phase space. The frequency of occurrence of these
self-encounters is determined by ergodicity. Permutation theory is used to
systematically sum over all topologically different families of such orbit
pairs. The resulting expansions of the form factor in powers of $\tau$ coincide
with the predictions of random-matrix theory, both for systems with and without
time-reversal invariance, and to all orders in $\tau$. Our results are closely
related to the zero-dimensional nonlinear $\sigma$ model of quantum field
theory. The relevant families of orbit pairs are in one-to-one correspondence
to Feynman diagrams appearing in the perturbative treatment of the $\sigma$
model.


title: Theory of Nonlinear Dispersive Waves and Selection of the Ground State

abstract:
  A theory of time dependent nonlinear dispersive equations of the Schroedinger
/ Gross-Pitaevskii and Hartree type is developed. The short, intermediate and
large time behavior is found, by deriving nonlinear Master equations (NLME),
governing the evolution of the mode powers, and by a novel multi-time scale
analysis of these equations. The scattering theory is developed and coherent
resonance phenomena and associated lifetimes are derived. Applications include
BEC large time dynamics and nonlinear optical systems. The theory reveals a
nonlinear transition phenomenon, ``selection of the ground state'', and NLME
predicts the decay of excited state, with half its energy transferred to the
ground state and half to radiation modes. Our results predict the recent
experimental observations of Mandelik et. al. in nonlinear optical waveguides.


title: Relaxation of nonlinear oscillations in BCS superconductivity

abstract:
  The diagonal case of the $sl(2)$ Richardson-Gaudin quantum pairing model
\cite{Richardson1,Richardson2,Richardson3,Richardson4,Richardson5,Richardson6,G
audin76} is known to be solvable as an Abel-Jacobi inversion problem
\cite{SOV,Kuznetzov,Kuz1,Kuz2,Kuz3,Kuz4,Kuz5,YAKE04}. This is an isospectral
(stationary) solution to a more general integrable hierarchy, in which the full
time evolution can be written as isomonodromic deformations. Physically, the
more general solution is appropriate when the single-particle electronic
spectrum is subject to external perturbations. The asymptotic behavior of the
nonlinear oscillations in the case of elliptic solutions is derived.


title:
Similarity transformations for Nonlinear Schrodinger Equations with time
  varying coefficients: Exact results

abstract:
  In this paper we use a similarity transformation connecting some families of
Nonlinear Schrodinger equations with time-varying coefficients with the
autonomous cubic nonlinear Schrodinger equation. This transformation allows one
to apply all known results for that equation to the non-autonomous case with
the additional dynamics introduced by the transformation itself. In particular,
using stationary solutions of the autonomous nonlinear Schrodinger equation we
can construct exact breathing solutions to multidimensional non-autonomous
nonlinear Schrodinger equations. An application is given in which we explicitly
construct time dependent coefficients leading to solutions displaying weak
collapse in three-dimensional scenarios. Our results can find physical
applicability in mean field models of Bose-Einstein condensates and in the
field of dispersion-managed optical systems.


title:
Partially integrable systems in multidimensions by a variant of the
  dressing method. 1

abstract:
  In this paper we construct nonlinear partial differential equations in more
than 3 independent variables, possessing a manifold of analytic solutions with
high, but not full, dimensionality. For this reason we call them ``partially
integrable''. Such a construction is achieved using a suitable modification of
the classical dressing scheme, consisting in assuming that the kernel of the
basic integral operator of the dressing formalism be nontrivial. This new
hypothesis leads to the construction of: 1) a linear system of compatible
spectral problems for the solution $U(\lambda;x)$ of the integral equation in 3
independent variables each (while the usual dressing method generates spectral
problems in 1 or 2 dimensions); 2) a system of nonlinear partial differential
equations in $n$ dimensions ($n>3$), possessing a manifold of analytic
solutions of dimension ($n-2$), which includes one largely arbitrary relation
among the fields. These nonlinear equations can also contain an arbitrary
forcing.


title: Integrable Vertex Models with General Twists

abstract:
  We review recent progress towards the solution of exactly solved isotropic
vertex models with arbitrary toroidal boundary conditions. Quantum space
transformations make it possible the diagonalization of the corresponding
transfer matrices by means of the quantum inverse scattering method. Explicit
expressions for the eigenvalues and Bethe ansatz equations of the twisted
isotropic spin chains based on the $B_n$, $D_n$ and $C_n$ Lie algebras are
presented. The applicability of this approach to the eight vertex model with
non-diagonal twists is also discussed.


title:
Synchronization from Disordered Driving Forces in Arrays of Coupled
  Oscillators

abstract:
  The effects of disorder in external forces on the dynamical behavior of
coupled nonlinear oscillator networks are studied. When driven synchronously,
i.e., all driving forces have the same phase, the networks display chaotic
dynamics. We show that random phases in the driving forces result in regular,
periodic network behavior. Intermediate phase disorder can produce network
synchrony. Specifically, there is an optimal amount of phase disorder, which
can induce the highest level of synchrony. These results demonstrate that the
spatiotemporal structure of external influences can control chaos and lead to
synchronization in nonlinear systems.


title: Hyperelliptic Theta-Functions and Spectral Methods

abstract:
  A code for the numerical evaluation of hyperelliptic theta-functions is
presented. Characteristic quantities of the underlying Riemann surface such as
its periods are determined with the help of spectral methods. The code is
optimized for solutions of the Ernst equation where the branch points of the
Riemann surface are parameterized by the physical coordinates. An exploration
of the whole parameter space of the solution is thus only possible with an
efficient code. The use of spectral approximations allows for an efficient
calculation of all quantities in the solution with high precision. The case of
almost degenerate Riemann surfaces is addressed. Tests of the numerics using
identities for periods on the Riemann surface and integral identities for the
Ernst potential and its derivatives are performed. It is shown that an accuracy
of the order of machine precision can be achieved. These accurate solutions are
used to provide boundary conditions for a code which solves the axisymmetric
stationary Einstein equations. The resulting solution agrees with the
theta-functional solution to very high precision.


title: Hyperelliptic Theta-Functions and Spectral Methods: KdV and KP solutions

abstract:
  This is the second in a series of papers on the numerical treatment of
hyperelliptic theta-functions with spectral methods. A code for the numerical
evaluation of solutions to the Ernst equation on hyperelliptic surfaces of
genus 2 is extended to arbitrary genus and general position of the branch
points. The use of spectral approximations allows for an efficient calculation
of all characteristic quantities of the Riemann surface with high precision
even in almost degenerate situations as in the solitonic limit where the branch
points coincide pairwise. As an example we consider hyperelliptic solutions to
the Kadomtsev-Petviashvili and the Korteweg-de Vries equation. Tests of the
numerics using identities for periods on the Riemann surface and the
differential equations are performed. It is shown that an accuracy of the order
of machine precision can be achieved.


title: A trihamiltonian extension of the Toda lattice

abstract:
  A new Poisson structure on a subspace of the Kupershmidt algebra is defined.
This Poisson structure, together with other two already known, allows to
construct a trihamiltonian recurrence for an extension of the periodic Toda
lattice with $n$ particles. Some explicit examples of the construction and of
the first integrals found in this way are given.


title:
Dynamics of two-component electromagnetic and acoustic extremely short
  pulses

abstract:
  The distinctive features of passing the two-component extremely short pulses
through the nonlinear media are discussed. The equations considered describe
the propagation in the two-level anisotropic medium of the electromagnetic
pulses consisting of ordinary and extraordinary components and an evolution of
the transverse-longitudinal acoustic pulses in a crystal containing the
paramagnetic impurities with effective spin S=1/2. The solutions decreasing
exponentially and algebraically are studied.


title: The Kirchhoff Rod as a XY Spin Chain Model

abstract:
  A XY Heisenberg spin chain model with two perpendicular spins par site is
mapped onto a Kirchhoff thin elastic rod. It is shown that in the case of
constant curvature the Euler--Lagrange equation leads to the static sine-Gordon
equation. The kink-antikink type and periodical static solutions for these
models are derived.


title:
Contraction Analysis of Time-Delayed Communications Using Simplified
  Wave Variables

abstract:
  We study stability of interacting nonlinear systems with time-delayed
communications, using contraction theory and a simplified wave variable design
inspired by robotic teleoperation. We show that contraction is preserved
through specific time-delayed feedback communications, and that this property
is independent of the values of the delays. The approach is then applied to
group cooperation with linear protocols, where it shown that synchronization
can be made robust to arbitrary time delays.


title: Infinite-Hamiltonian Structures of the Riemann Equation

abstract:
  We give two distinct infinite-Hamiltonian representations for the Riemann
equation. One with first order Hamiltonian operators and another with third
order-first order Hamiltonian operators. Both representations contain an
arbitrary function of the dynamical variable. We prove that all the Hamiltonian
operators of the Riemann equation are mutually compatible.


title:
Third-order integrable difference equations generated by a pair of
  second-order equations

abstract:
  We show that the third-order difference equations proposed by Hirota,
  Kimura and Yahagi are generated by a pair of second-order difference
equations. In some cases, the pair of the second-order equations are equivalent
to the Quispel-Robert-Thomson(QRT) system, but in the other cases, they are
irrelevant to the QRT system. We also discuss an ultradiscretization of the
equations.


title:
Analytical Expression for Low-dimensional Resonance Island in
  4-dimensional Symplectic Map

abstract:
  We study a 2- and a 4-dimensional nearly integrable symplectic maps using a
singular perturbation method. Resonance island structures in the 2- and 4-
dimensional maps are successfully obtained. Those perturbative results are
numerically confirmed.


title: On the heavenly equation hierarchy and its reductions

abstract:
  Second heavenly equation hierarchy is considered using the framework of
hyper-K\"ahler hierarchy developed by Takasaki. Generating equations for the
hierarchy are introduced, they are used to construct generating equations for
reduced hierarchies. General $N$-reductions, logarithmic reduction and rational
reduction for one of the Lax-Sato functions are discussed. It is demonstrated
that rational reduction is equivalent to the symmetry constraint.


title:
Chaotic maps coupled with random delays: connectivity, topology, and
  network propensity for synchronization

abstract:
  We study the influence of network topology and connectivity on the
synchronization properties of chaotic logistic maps, interacting with random
delay times. Four different types of topologies are investigated: two regular
(a ring-type and a ring-type with a central node) and two random (free-scale
Barabasi-Albert and small-world Newman-Watts). The influence of the network
connectivity is studied by varying the average number of links per node, while
keeping constant the total input that each map receives from its neighbors. For
weak coupling the array does not synchronize regardless the topology or
connectivity of the network; however, for certain connectivity values there is
enhanced coherence. For strong coupling the array synchronizes in the
homogeneous steady-state, where the chaotic dynamics of the individual maps is
suppressed. For both, weak and strong coupling, the array propensity for
synchronization is largely independent of the network topology and depends
mainly on the average number of links per node.


title:
On linear stability of steady space-periodic magnetohydrodynamic systems
  to perturbations involving large periods

abstract:
  I construct a complete asymptotic expansion of solutions to the problem of
linear stability of three-dimensional steady space-periodic magnetohydrodynamic
states to perturbations involving large periods. Eddy diffusivity tensor is
derived for parity-invariant steady states. I present numerical evidences that
if perturbations of the flow are permitted, then the effect of negative eddy
diffusivity emerges at much larger magnetic molecular diffusivities than in the
kinematic dynamo problem (where no perturbations of the flow are assumed).


title: Nonassociativity and Integrable Hierarchies

abstract:
  Let A be a nonassociative algebra such that the associator (A,A^2,A)
vanishes. If A is freely generated by an element f, there are commuting
derivations delta_n, n=1,2,..., such that delta_n(f) is a nonlinear homogeneous
polynomial in f of degree n+1. We prove that the expressions delta_{n_1} ...
delta_{n_k}(f) satisfy identities which are in correspondence with the
equations of the Kadomtsev-Petviashvili (KP) hierarchy. As a consequence,
solutions of the `nonassociative hierarchy' partial_{t_n}(f) = delta_n(f),
n=1,2,..., of ordinary differential equations lead to solutions of the KP
hierarchy. The framework is extended by introducing the notion of an A-module
and constructing, with the help of the derivations delta_n, zero curvature
connections and linear systems.


title: On Engineering and Emergence

abstract:
  The engineering and design of self-organizing systems with emergent
properties is a long-standing problem in the field of complex and distributed
systems, for example in the engineering of self-organizing Multi-Agent Systems.
The problem of combining engineering with emergence - to find a simple rule for
a complex pattern - equals the problem of science in general. Therefore the
answers are similar, and the scientific method is the general solution to the
problem of engineering complex systems.


title: Duality for the general isomonodromy problem

abstract:
  By an extension of Harnad's and Dubrovin's `duality' constructions, the
general isomonodromy problem studied by Jimbo, Miwa, and Ueno is equivalent to
one in which the linear system of differential equations has a regular
singularity at the origin and an irregular singularity at infinity (both
resonant). The paper looks at this dual formulation of the problem from two
points of view: the symplectic geometry of spaces associated with the loop
group of the general linear group, and a generalization of the self-dual
Yang-Mills equations.


title:
Stretching of polymers around the Kolmogorov scale in a turbulent shear
  flow

abstract:
  We present numerical studies of stretching of Hookean dumbbells in a
turbulent Navier-Stokes flow with a linear mean profile, <u_x>=Sy. In addition
to the turbulence features beyond the viscous Kolmogorov scale \eta, the
dynamics at the equilibrium extension of the dumbbells significantly below eta
is well resolved. The variation of the constant shear rate S causes a change of
the turbulent velocity fluctuations on all scales and thus of the intensity of
local stretching rate of the advecting flow. The latter is measured by the
maximum Lyapunov exponent lambda_1 which is found to increase as \lambda_1 ~
S^{3/2}, in agreement with a dimensional argument. The ensemble of up to 2
times 10^6 passively advected dumbbells is advanced by Brownian dynamics
simulations in combination with a pseudospectral integration for the turbulent
shear flow. Anisotropy of stretching is quantified by the statistics of the
azimuthal angle $\phi$ which measures the alignment with the mean flow axis in
the x-y shear plane, and the polar angle theta which determines the orientation
with respect to the shear plane. The asymmetry of the probability density
function (PDF) of phi increases with growing shear rate S. Furthermore, the PDF
becomes increasingly peaked around mean flow direction (phi= 0). In contrast,
the PDF of the polar angle theta is symmetric and less sensitive to changes of
S.


title: Reinforcement learning of recurrent neural network for temporal coding

abstract:
  We study a reinforcement learning for temporal coding with neural network
consisting of stochastic spiking neurons. In neural networks, information can
be coded by characteristics of the timing of each neuronal firing, including
the order of firing or the relative phase differences of firing. We derive the
learning rule for this network and show that the network consisting of
Hodgkin-Huxley neurons with the dynamical synaptic kinetics can learn the
appropriate timing of each neuronal firing. We also investigate the system size
dependence of learning efficiency.


title: Ballistic aggregation in symmetric and non-symmetric flows

abstract:
  We consider exact solutions to the problem of ballistic aggregation in a flow
of adhesive particles, providing a model for large-scale structure formation in
cosmology within the framework of the Zel'dovich approximation. Two different
explicit variational constructions, suggested for this problem by (A.
Shnirelman, 1986) and (E Weinan et al, 1996) in the case of flat symmetry, are
shown to be equivalent. Explicit solutions are constructed for flows of
cylindric and spherical symmetry. Two explicit counterexamples, showing that
natural generalizations of both variational constructions fail to provide
solutions for nonsymmetric multidimensional flows, are presented.


title: Lax Integrable Supersymmetric Hierarchies on Extented Phase Spaces

abstract:
  We obtain via B\"acklund transformation the Hamiltonian representation for a
Lax type nonlinear dynamical system hierarchy on a dual space to the Lie
algebra of super-integral-differential operators of one anticommuting variable,
extended by evolutions of the corresponding spectral problem eigenfunctions and
adjoint eigenfunctions, as well as for the hierarchies of their additional
symmetries. The relation of these hierarchies with the integrable by Lax
(2|1+1)-dimensional supersymmetric Davey-Stewartson system is investigated.


title:
Stickiness in Hamiltonian systems: from sharply divided to hierarchical
  phase space

abstract:
  We investigate the dynamics of chaotic trajectories in simple yet physically
important Hamiltonian systems with non-hierarchical borders between regular and
chaotic regions with positive measures. We show that the stickiness to the
border of the regular regions in systems with such a sharply divided phase
space occurs through one-parameter families of marginally unstable periodic
orbits and is characterized by an exponent \gamma= 2 for the asymptotic
power-law decay of the distribution of recurrence times. Generic perturbations
lead to systems with hierarchical phase space, where the stickiness is
apparently enhanced due to the presence of infinitely many regular islands and
Cantori. In this case, we show that the distribution of recurrence times can be
composed of a sum of exponentials or a sum of power-laws, depending on the
relative contribution of the primary and secondary structures of the hierarchy.
Numerical verification of our main results are provided for area-preserving
maps, mushroom billiards, and the newly defined magnetic mushroom billiards.


title: Testing the assumptions of linear prediction analysis in normal vowels

abstract:
  This paper develops an improved surrogate data test to show experimental
evidence, for all the simple vowels of US English, for both male and female
speakers, that Gaussian linear prediction analysis, a ubiquitous technique in
current speech technologies, cannot be used to extract all the dynamical
structure of real speech time series. The test provides robust evidence
undermining the validity of these linear techniques, supporting the assumptions
of either dynamical nonlinearity and/or non-Gaussianity common to more recent,
complex, efforts at dynamical modelling speech time series. However, an
additional finding is that the classical assumptions cannot be ruled out
entirely, and plausible evidence is given to explain the success of the linear
Gaussian theory as a weak approximation to the true, nonlinear/non-Gaussian
dynamics. This supports the use of appropriate hybrid
linear/nonlinear/non-Gaussian modelling. With a calibrated calculation of
statistic and particular choice of experimental protocol, some of the known
systematic problems of the method of surrogate data testing are circumvented to
obtain results to support the conclusions to a high level of significance.


title: Ruelle-Pollicott resonances for real analytic hyperbolic map

abstract:
  We study two simple real analytic uniformly hyperbolic dynamical systems:
expanding maps on the circle S1 and hyperbolic maps on the torus T2. We show
that the Ruelle-Pollicott resonances which describe time correlation functions
of the chaotic dynamics can be obtained as the eigenvalues of a trace class
operator in Hilbert space L2(S1) or L2(T2) respectively. The trace class
operator is obtained by conjugation of the Ruelle transfer operator in a
similar way quantum resonances are obtained in open quantum systems. We comment
this analogy.


title: Notes on Contraction Theory

abstract:
  These notes derive a number of technical results on nonlinear contraction
theory, a comparatively recent tool for system stability analysis. In
particular, they provide new results on the preservation of contraction through
system combinations, a property of interest in modelling biological systems.


title:
Weakly nonlinear stability of magnetohydrodynamic systems with a center
  of symmetry to perturbations, involving large scales

abstract:
  I consider the problem of weakly nonlinear stability of three-dimensional
parity-invariant magnetohydrodynamic systems to perturbations, involving large
scales. I assume that the MHD state, the stability of which I investigate, does
not involve large spatio-temporal scales, and it is stable to perturbations
involving the same small spatial scales, as the perturbed MHD state. Mean-field
equations, which I derive for the perturbation using asymptotic techniques for
multiscale systems, are a generalization of the standard equations of
magnetohydrodynamics (the Navier-Stokes equation with the Lorentz force and the
magnetic induction equation). In them, the operator of combined eddy
diffusivity emerges, which is in general anisotropic and not necessarily
negatively defined, and new quadratic terms, analogous to the ones describing
advection. A method for efficient computation of coefficients of the eddy
diffusivity tensor and eddy advection terms in the mean-field equations is
proposed.


title:
Weakly nonlinear stability of convective magnetohydrodynamic systems
  without alpha-effect to perturbations involving large scales

abstract:
  I consider the problem of weakly nonlinear stability of three-dimensional
convective magnetohydrodynamic systems, where there is no alpha-effect or it is
insignificant, to perturbations involving large scales. I assume that the
convective MHD state (steady or evolutionary), the stability of which I
investigate, does not involve large spatio-temporal scales, and it is stable to
perturbations involving the same small spatial scales, as the perturbed state.
Mean-field equations, which I derive for the perturbation using asymptotic
techniques for multiscale systems, are a generalization of the equations of
magnetohydrodynamics (the Navier-Stokes and magnetic induction equations). The
operator of combined eddy diffusivity emerges, which is in general anisotropic
and not necessarily negatively defined, as well as new quadratic terms
analogous to the ones describing advection.


title: The Bi-Hamiltonian Structure of the Short Pulse Equation

abstract:
  We prove the integrability of the short pulse equation derived recently by
Sch\"afer and Wayne from a hamiltonian point of view. We give its
bi-hamiltonian structure and show how the recursion operator defined by the
hamiltonian operators is connected with the one obtained by Sakovich and
Sakovich. An alternative zero-curvature formulation is also given.


title: The Short Pulse Hierarchy

abstract:
  We study a new hierarchy of equations containing the Short Pulse equation,
which describes the evolution of very short pulses in nonlinear media, and the
Elastic Beam equation, which describes nonlinear transverse oscillations of
elastic beams under tension. We show that the hierarchy of equations is
integrable. We obtain the two compatible Hamiltonian structures. We construct
an infinite series of both local and nonlocal conserved charges. A Lax
description is presented for both systems. For the Elastic Beam equations we
also obtain a nonstandard Lax representation.


title: Hexaroll chaos in inclined layer convection

abstract:
  We report experimental observations of hexaroll chaos in inclined layer
convection. Two separate populations of defect complexes characterize the
defect turbulent state, one the classical penta-hepta defect of hexagonal
planform patterns, and the other a short-lived complex capable of
self-annihilation. By measuring the defect statistics we show that short-lived
defect complexes give rise to linear defect destruction rates. This observation
explains previous results in other defect-turbulent pattern forming systems.


title:
Wave energy localization by self-focusing in large molecular structures:
  a damped stochastic discrete nonlinear Schroedinger equation model

abstract:
  Wave self-focusing in molecular systems subject to thermal effects, such as
thin molecular films and long biomolecules, can be modeled by stochastic
versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott,
and this can be approximated by continuum limits in the form of stochastic
nonlinear Schroedinger equations.
  Previous studies directed at the SNLS approximations have indicated that the
self-focusing of wave energy to highly localized states can be inhibited by
phase noise (modeling thermal effects) and can be restored by phase damping
(modeling heat radiation).
  We show that the continuum limit is probably ill-posed in the presence of
spatially uncorrelated noise, at least with little or no damping, so that
discrete models need to be addressed directly. Also, as has been noted by other
authors, omission of damping produces highly unphysical results.
  Numerical results are presented for the first time for the discrete models
including the highly nonlinear damping term, and new numerical methods are
introduced for this purpose. Previous conjectures are in general confirmed, and
the damping is shown to strongly stabilize the highly localized states of the
discrete models. It appears that the previously noted inhibition of nonlinear
wave phenomena by noise is an artifact of modeling that includes the effects of
heat, but not of heat loss.


title: Wavevector resonance in a nonlinear multi-wavespeed chaotic billiard

abstract:
  Nonlinear coupling between eigenmodes of a system leads to spectral energy
redistribution. For multi-wavespeed chaotic billiards the average coupling
strength can exhibit sharp discontinuities as a function of frequency related
to wavevector coincidences between constituent waves of different wavespeeds.
The phenomenon is investigated numerically for an ensemble of 2D square
two-wavespeed billiards with rough boundaries and quadratic nonlinearity
representative of elastodynamic waves. Results of direct numerical simulations
are compared with theoretical predictions.


title: Solitary wave solutions of the short pulse equation

abstract:
  An exact nonsingular solitary wave solution of the Schafer-Wayne short pulse
equation is derived from the breather solution of the sine-Gordon equation by
means of a transformation between these two integrable equations.

categories: nlin.SI math-ph math.MP nlin.PS physics.optics


title: Anomalous slow fidelity decay for symmetry breaking perturbations

abstract:
  Symmetries as well as other special conditions can cause anomalous slowing
down of fidelity decay. These situations will be characterized, and a family of
random matrix models to emulate them generically presented. An analytic
solution based on exponentiated linear response will be given. For one
representative case the exact solution is obtained from a supersymmetric
calculation. The results agree well with dynamical calculations for a kicked
top.


title: Solitary and compact-like shear waves in the bulk of solids

abstract:
  We show that a model proposed by Rubin, Rosenau, and Gottlieb [J. Appl. Phys.
77 (1995) 4054], for dispersion caused by an inherent material characteristic
length, belongs to the class of simple materials. Therefore, it is possible to
generalize the idea of Rubin, Rosenau, and Gottlieb to include a wide range of
material models, from nonlinear elasticity to turbulence. Using this insight,
we are able to fine-tune nonlinear and dispersive effects in the theory of
nonlinear elasticity in order to generate pulse solitary waves and also bulk
travelling waves with compact support.


title: Duality between quantum and classical dynamics for integrable billiards

abstract:
  We establish a duality between the quantum wave vector spectrum and the
eigenmodes of the classical Liouvillian dynamics for integrable billiards.
Signatures of the classical eigenmodes appear as peaks in the correlation
function of the quantum wave vector spectrum. A semiclassical derivation and
numerical calculations are presented in support of the results. These classical
eigenmodes can be observed in physical experiments through the auto-correlation
of the transmission coefficient of waves in quantum billiards. Exact classical
trace formulas of the resolvent are derived for the rectangle, equilateral
triangle, and circle billiards. We also establish a correspondence between the
classical periodic orbit length spectrum and the quantum spectrum for
integrable polygonal billiards.


title:
Synchronized bursts following instability of synchronous spiking in
  chaotic neuronal networks

abstract:
  We report on the origin of synchronized bursting dynamics in various networks
of neural spiking oscillators, when a certain threshold in coupling strength is
exceeded. These ensembles synchronize at relatively low coupling strength and
lose synchronization at stronger coupling via spatio-temporal intermittency.
The latter transition triggers multiple-timescale dynamics, which results in
synchronized bursting with a fractal-like spatio-temporal pattern of spiking.
Implementation of an appropriate technique of separating oscillations on
different time-scales allows for quantitative analysis of this phenomenon. We
show, that this phenomenon is generic for various network topologies from
regular to small-world and scale-free ones and for different types of coupling.


title: Fractal in the statistics of Goldbach partition

abstract:
  Some interesting chaos phenomena have been found in the difference of prime
numbers. Here we discuss a theme about the sum of two prime numbers, Goldbach
conjecture. This conjecture states that any even number could be expressed as
the sum of two prime numbers. Goldbach partition r(n) is the number of
representations of an even number n as the sum of two primes. This paper
analyzes the statistics of series r(n) (n=4,6,8,...). The familiar 3 period
oscillations in histogram of difference of consecutive primes appear in r(n).We
also find r(n) series could be divided into different levels period oscillation
series. The series in the same or different levels are all very similar, which
presents the obvious fractal phenomenon. Moreover, symmetry between the
statistics figure of sum and difference of two prime numbers are also
described. We find the estimate of Hardy-Littlewood could precisely depict
these phenomena. A rough analyzing for periodic behavior of r(n) is given by
symbolic dynamics theory at last.


title:
Strongly nonlinear nature of interfacial-surfactant instability of
  Couette flow

abstract:
  Nonlinear stages of the recently uncovered instability due to insoluble
surfactant at the interface between two fluids are investigated for the case of
a creeping plane Couette flow with one of the fluids a thin film and the other
one a much thicker layer. Numerical simulation of strongly nonlinear longwave
evolution equations which couple the film thickness and the surfactant
concentration reveals that in contrast to all similar instabilities of
surfactant-free flows, no amount of the interfacial shear rate can lead to a
small-amplitude saturation of the instability. Thus, the flow is stable when
the shear is zero, but with non-zero shear rates, no matter how small or large
(while remaining below an upper limit set by the assumption of creeping flow),
it will reach large deviations from the base values-- of the order of the
latter or larger. It is conjectured that the time this evolution takes grows to
infinity as the interfacial shear approaches zero. It is verified that the
absence of small-amplitude saturation is not a singularity of the zero surface
diffusivity of the interfacial surfactant.


title:
Experimental characterization of domain walls dynamics in a
  photorefractive oscillator

abstract:
  We report the experimental characterization of domain walls dynamics in a
photorefractive resonator in a degenerate four wave mixing configuration. We
show how the non flat profile of the emitted field affects the velocity of
domain walls as well as the variations of intensity and phase gradient during
their motion. We find a clear correlation between these two last quantities
that allows the experimental determination of the chirality that governs the
domain walls dynamics.


title: Dynamics and statistics of heavy particles in turbulent flows

abstract:
  We present the results of Direct Numerical Simulations (DNS) of turbulent
flows seeded with millions of passive inertial particles. The maximum Taylor's
Reynolds number is around 200. We consider particles much heavier than the
carrier flow in the limit when the Stokes drag force dominates their dynamical
evolution. We discuss both the transient and the stationary regimes. In the
transient regime, we study the growt of inhomogeneities in the particle spatial
distribution driven by the preferential concentration out of intense vortex
filaments. In the stationary regime, we study the acceleration fluctuations as
a function of the Stokes number in the range [0.16:3.3]. We also compare our
results with those of pure fluid tracers (St=0) and we find a critical behavior
of inertia for small Stokes values. Starting from the pure monodisperse
statistics we also characterize polydisperse suspensions with a given mean
Stokes.


title: Dynamics of precipitation pattern formation at geothermal hot springs

abstract:
  We formulate and model the dynamics of spatial patterns arising during the
precipitation of calcium carbonate from a supersaturated shallow water flow.
The model describes the formation of travertine deposits at geothermal hot
springs and rimstone dams of calcite in caves. We find explicit solutions for
travertine domes at low flow rates, identify the linear instabilities which
generate dam and pond formation on sloped substrates, and present simulations
of statistical landscape evolution.


title: Diffusion-induced spontaneous pattern formation on gelation surfaces

abstract:
  Although the pattern formation on polymer gels has been considered as a
result of the mechanical instability due to the volume phase transition, we
found a macroscopic surface pattern formation not caused by the mechanical
instability. It develops on gelation surfaces, and we consider the
reaction-diffusion dynamics mainly induces a surface instability during
polymerization. Random and straight stripe patterns were observed, depending on
gelation conditions. We found the scaling relation between the characteristic
wavelength and the gelation time. This scaling is consistent with the
reaction-diffusion dynamics and would be a first step to reveal the gelation
pattern formation dynamics.


title:
Chaotic Vibration of a Quarter-Car Model Excited by the Road Surface
  Profile

abstract:
  The Melnikov criterion is used to examine a global homoclinic bifurcation and
transition to chaos in the case of a quarter car model excited kinematically by
the road surface profile. By analyzing the potential an analytic expression is
found for the homoclinic orbit. By introducing an harmonic excitation term and
damping as perturbations, the critical Melnikov amplitude of the road surface
profile is found, above which the system can vibrate chaotically.


title:
Pulsive feedback control for stabilizing unstable periodic orbits in a
  nonlinear oscillator with a non-symmetric potential

abstract:
  We examine a strange chaotic attractor and its unstable periodic orbits in
case of one degree of freedom nonlinear oscillator with non symmetric
potential. We propose an efficient method of chaos control stabilizing these
orbits by a pulsive feedback technique. Discrete set of pulses enable us to
transfer the system from one periodic state to another.


title:
Transition to Chaos in the Self-Excited System with a Cubic Double Well
  Potential and Parametric Forcing

abstract:
  We examine the Melnikov criterion for a global homoclinic bifurcation and a
possible transition to chaos in case of a single degree of freedom nonlinear
oscillator with a symmetric double well nonlinear potential. The system was
subjected simultaneously to parametric periodic forcing and self excitation via
negative damping term. Detailed numerical studies confirm the analytical
predictions and show that transitions from regular to chaotic types of motion
are often associated with increasing the energy of an oscillator and its escape
from a single well.


title: Vibration of the Duffing Oscillator: Effect of Fractional Damping

abstract:
  We have applied the Melnikov criterion to examine a global homoclinic
bifurcation and transition to chaos in a case of the Duffing system with
nonlinear fractional damping and external excitation.
  Using perturbation methods we have found a critical forcing amplitude above
which the system may behave chaotically.
  The results have been verified by numerical simulations using standard
nonlinear tools as
  Poincare maps and a Lyapunov exponent. Above the critical Melnikov amplitude
$\mu_c$, which is the sufficient condition of a global homoclinic bifurcation,
we have observed the region with a transient chaotic motion.


title: Breathers or quasibreathers?

abstract:
  For the James breathers in the K2-K3-K4 chain and for breathers in the
K4-chain, we prove numerically that these dynamical objects are not strictly
time-periodic. Indeed, for the both cases, there exist certain deviations in
the vibrational frequencies of the individual particles, which certainly exceed
the possible numerical errors. We refer to the dynamical objects with such
properties as quasibreathers. For the K4-chain, a rigorous investigation of
existence and stability of the breathers and quasibreathers is presented. In
particular, it is proved that they are stable up to a certain strength of the
intersite part of the potential with respect to its on-site part. We conjecture
that the main results of this paper are also valid in the general case and,
therefore, it seems that one must speak about quasibreathers rather than about
strictly time-periodic breathers.


title: Polygons for finding exact solutions of nonlinear differential equations

abstract:
  New method for finding exact solutions of nonlinear differential equations is
presented. It is based on constructing the polygon corresponding to the
equation studied. The algorithms of power geometry are used. The method is
applied for finding one -- parameter exact solutions of the generalized
Korteveg -- de Vries -- Burgers equation, the generalized Kuramoto -
Sivashinsky equation, and the fifth -- order nonlinear evolution equation. All
these nonlinear equations contain the term $u^mu_x$. New exact solitary waves
are found.


title: On Linearizing Systems of Diffusion Equations

abstract:
  We consider systems of diffusion equations that have considerable interest in
Soil Science and Mathematical Biology and focus upon the problem of finding
those forms of this class that can be linearized. In particular we use the
equivalence transformations of the second generation potential system to derive
forms of this system that can be linearized. In turn, these transformations
lead to nonlocal mappings that linearize the original system.


title:
Fidelity freeze for a random matrix model with off--diagonal
  perturbation

abstract:
  The concept of fidelity has been introduced to characterize the stability of
a quantum-mechanical system against perturbations. The fidelity amplitude is
defined as the overlap integral of a wave packet with itself after the
development forth and back under the influence of two slightly different
Hamiltonians. It was shown by Prosen and Znidaric in the linear-response
approximation that the decay of the fidelity is frozen if the Hamiltonian of
the perturbation contains off-diagonal elements only. In the present work the
results of Prosen and Znidaric are extended by a supersymmetry calculation to
arbitrary strengths of the perturbation for the case of an unperturbed
Hamiltonian taken from the Gaussian orthogonal ensemble and a purely unitary
antisymmetric perturbation. It is found that for the exact calculation the
freeze of fidelity is only slightly reduced as compared to the linear-response
approximation. This may have important consequences for the design of quantum
computers.


title:
Border Collision Bifurcations in n-Dimensional Piecewise Linear
  Discontinuous Maps

abstract:
  In this paper we report some important results that help in analizing the
border collision bifurcations that occur in n-dimensional discontinuous maps.
For this purpose, we use the piecewise linear approximation in the neighborhood
of the plane of discontinuity. Earlier, Feigin had made a similar analysis for
general n-dimensional piecewise smooth continuous maps. Proceeding along
similar lines, we obtain the general conditions of existence of period-1 and
period-2 fixed points before and after a border collision bifurcation. The
application of the method is then illustrated using a specific example of a
two-dimensional discontinuous map.


title:
The Algebro-Geometric Toda Hierarchy Initial Value Problem for
  Complex-Valued Initial Data

abstract:
  We discuss the algebro-geometric initial value problem for the Toda hierarchy
with complex-valued initial data and prove unique solvability globally in time
for a set of initial (Dirichlet divisor) data of full measure. To this effect
we develop a new algorithm for constructing stationary complex-valued
algebro-geometric solutions of the Toda hierarchy, which is of independent
interest as it solves the inverse algebro-geometric spectral problem for
generally non-self-adjoint Jacobi operators, starting from a suitably chosen
set of initial divisors of full measure. Combined with an appropriate
first-order system of differential equations with respect to time (a substitute
for the well-known Dubrovin equations), this yields the construction of global
algebro-geometric solutions of the time-dependent Toda hierarchy.
  The inherent non-self-adjointness of the underlying Lax (i.e., Jacobi)
operator associated with complex-valued coefficients for the Toda hierarchy
poses a variety of difficulties that, to the best of our knowledge, are
successfully overcome here for the first time. Our approach is not confined to
the Toda hierarchy but applies generally to 1+1-dimensional completely
integrable (discrete and continuous) soliton equations.


title:
Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist
  Map

abstract:
  The breakup of shearless invariant tori with winding number
$\omega=[0,1,11,1,1,...]$ (in continued fraction representation) of the
standard nontwist map is studied numerically using Greene's residue criterion.
Tori of this winding number can assume the shape of meanders (folded-over
invariant tori which are not graphs over the x-axis in $(x,y)$ phase space),
whose breakup is the first point of focus here. Secondly, multiple shearless
orbits of this winding number can exist, leading to a new type of breakup
scenario. Results are discussed within the framework of the renormalization
group for area-preserving maps. Regularity of the critical tori is also
investigated.


title:
Semi-discrete composite solitons in arrays of quadratically nonlinear
  waveguides

abstract:
  We demonstrate that an array of discrete waveguides on a slab substrate, both
featuring the $\chi^{2}$ nonlinearity, supports stable solitons composed of
discrete and continuous components. Two classes of fundamental composite
solitons are identified: ones consisting of a discrete fundamental-frequency
(FF) component in the waveguide array, coupled to a continuous second-harmonic
(SH) component in the slab waveguide, and solitons with an inverted FF/SH
structure. Twisted bound states of the fundamental solitons are found too. In
contrast with usual systems, the \emph{intersite-centered} fundamental solitons
and bound states with the twisted continuous components are stable, in an
almost entire domain of their existence.


title:
Drift of particles in self-similar systems and its Liouvillian
  interpretation

abstract:
  We study the dynamics of classical particles in different classes of
spatially extended self-similar systems, consisting of (i) a self-similar
Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master
equation. In all three systems the particles typically drift at constant
velocity and spread ballistically. These transport properties are analyzed in
terms of the spectral properties of the operator evolving the probability
densities. For systems (i) and (ii), we explain the drift from the properties
of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors


title: Reducing or enhancing chaos using periodic orbits

abstract:
  A method to reduce or enhance chaos in Hamiltonian flows with two degrees of
freedom is discussed. This method is based on finding a suitable perturbation
of the system such that the stability of a set of periodic orbits changes
(local bifurcations). Depending on the values of the residues, reflecting their
linear stability properties, a set of invariant tori is destroyed or created in
the neighborhood of the chosen periodic orbits. An application on a
paradigmatic system, a forced pendulum, illustrates the method.


title: Discrete soliton ratchets driven by biharmonic fields

abstract:
  Directed motion of topological solitons (kinks or antikinks) in the damped
and AC-driven discrete sine-Gordon system is investigated. We show that if the
driving field breaks certain time-space symmetries, the soliton can perform
unidirectional motion. The phenomenon resembles the well known effects of
ratchet transport and nonlinear harmonic mixing. Direction of the motion and
its velocity depends on the shape of the AC drive. Necessary conditions for the
occurrence of the effect are formulated. In comparison with the previously
studied continuum case, the discrete case shows a number of new features:
non-zero depinning threshold for the driving amplitude, locking to the rational
fractions of the driving frequency, and diffusive ratchet motion in the case of
weak intersite coupling.


title: Abrupt transition in a sandpile model

abstract:
  We present a fixed energy sandpile (FES) model which, by increasing the
initial energy,undergoes, at the level of individual configurations, a
discontinuous transition.The model is obtained by modifying the toppling
procedure in the BTW rules: the energy transfer from a toppling site takes
place only to neighbouring sites with less energy (negative gradient
constraint) and with a time ordering (asynchronous). The model is minimal in
the sense that removing either of the two above mentioned constraints (negative
gradient or time ordering) the abrupt transition goes over to a continuous
transition as in the usual BTW case. Therefore the proposed model offers an
unique possibility to explore at the microscopic level the basic mechanisms
underlying discontinuous transitions.


title: On classification of integrable non-evolutionary equations

abstract:
  We study partial differential equations of second order (in time) that
possess a hierarchy of infinitely many higher symmetries. The famous Boussinesq
equation is a member of this class after the extension of the differential
polynomial ring. We develop the perturbative symmetry approach in symbolic
representation. Applying it, we classify the integrable equations of 4th and
6th order (in the space derivative) equations, as well as we have found three
new 10th order integrable equations. To prove the integrability we provide the
corresponding bi-Hamiltonian structures and recursion operators.


title: Partially integrable nonlinear equations with one higher symmetry

abstract:
  In this paper we present a family of second order in time nonlinear partial
differential equations, which have only one higher symmetry. These equations
are not integrable, but have a solution depending on one arbitrary function.


title:
Self-Organization and Finite Velocity of Transmitting Substance and
  Energy through Space-Time

abstract:
  The idea that the velocity of transmitting substance/energy trough space-time
is to be bounded is a fundamental concept in the science. To the most surprise,
it turns out that it is not always met. We demonstrate that the existing
approaches to the self-organization, another major concept in the science, let
the velocity of transmitting substance to be arbitrary. Further we prove that
only the boundedness of the velocity is not enough to ensure the
self-organization. That is why we develop radically novel approach to the
macroscopic evolution that not only reconciles the self-organization and the
velocity ansatz but in addition gives physically credible basis to phenomena
like Feigenbaum cascade and fluctuation-assisted bifurcations.

categories: nlin.AO cond-mat.stat-mech math-ph math.MP physics.gen-ph


title: Driving convection by a temperature gradient or a heat current

abstract:
  Bifurcation properties, stability behavior, dynamics, and the heat transfer
of convection structures in a horizontal fluid layer that is driven away from
thermal equilibrium by imposing a vertical temperature difference are compared
with those resulting from imposing a heat current. In particular oscillatory
convection that occurs in binary fluid mixtures in the form of travelling and
standing waves is determined numerically for the two different driving
mechanisms. Conditions are elucidated under which current driven convection is
stable while temperature driven convection is unstable.


title: The deformations of Whitham systems and Lagrangian formalism

abstract:
  We consider the Lagrangian formalism of the deformations of Whitham systems
having Dubrovin-Zhang form. As an example the case of modulated one-phase
solutions of the non-linear "V-Gordon" equation is considered.


title: Chaotic Cryptographic Scheme Based on Composition Maps

abstract:
  In recent years, a growing number of cryptosystems based on chaos have been
proposed. But most of them encountered many problems such as small key space
and weak security. In the present paper, a new kind of chaotic cryptosystem
based on Composition of Trigonometric Chaotic Maps is proposed. These maps
which are defined as ratios of polynomials of degree N, have interesting
properties such as invariant measure, ergodicity, variable chaotic region with
respect to the control parameters and ability to construct composition form of
maps. We have used a composition of chaotic map to shuffle the position of
image pixels. Another composition of chaotic map is used in diffusion process.
According to the performed analysis, the introduced algorithm can satisfy the
required performances such as high level security, large key space and the
acceptable encryption speed.


title: Steepness and spectrum of nonlinear deformed shallow water wave

abstract:
  Process of the nonlinear deformation of the shallow water wave in a basin of
constant depth is studied. The characteristics of the first breaking are
analyzed in details. The Fourier spectrum and steepness of the nonlinear wave
is calculated. It is shown that spectral amplitudes can be expressed through
the wave front steepness, and this can be used for practical estimations.


title: Quasi-exact solvability beyond the SL(2) algebraization

abstract:
  We present evidence to suggest that the study of one dimensional
quasi-exactly solvable (QES) models in quantum mechanics should be extended
beyond the usual $\sla(2)$ approach. The motivation is twofold: We first show
that certain quasi-exactly solvable potentials constructed with the $\sla(2)$
Lie algebraic method allow for a new larger portion of the spectrum to be
obtained algebraically. This is done via another algebraization in which the
algebraic hamiltonian cannot be expressed as a polynomial in the generators of
$\sla(2)$. We then show an example of a new quasi-exactly solvable potential
which cannot be obtained within the Lie-algebraic approach.


title:
Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear
  media

abstract:
  We demonstrate the existence of stable three-dimensional spatiotemporal
solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental
(nonspinning) STSs forming one-parameter families are stable if their
propagation constant exceeds a certain critical value, that is inversely
proportional to the range of nonlocality of nonlinear response. All spinning
three-dimensional STSs are found to be unstable.


title: Uni-directional transport properties of a serpent billiard

abstract:
  We present a dynamical analysis of a classical billiard chain -- a channel
with parallel semi-circular walls, which can serve as a model for a bended
optical fiber. An interesting feature of this model is the fact that the phase
space separates into two disjoint invariant components corresponding to the
left and right uni-directional motions. Dynamics is decomposed into the jump
map -- a Poincare map between the two ends of a basic cell, and the time
function -- traveling time across a basic cell of a point on a surface of
section. The jump map has a mixed phase space where the relative sizes of the
regular and chaotic components depend on the width of the channel. For a
suitable value of this parameter we can have almost fully chaotic phase space.
We have studied numerically the Lyapunov exponents, time auto-correlation
functions and diffusion of particles along the chain. As a result of a
singularity of the time function we obtain marginally-normal diffusion after we
subtract the average drift. The last result is also supported by some
analytical arguments.


title: New symmetries for the Ablowitz-Ladik hierarchies

abstract:
  In the letter we give new symmetries for the isospectral and non-isospectral
Ablowitz-Ladik hierarchies by means of the zero curvature representations of
evolution equations related to the Ablowitz-Ladik spectral problem. Lie
algebras constructed by symmetries are further obtained. We also discuss the
relations between the recursion operator and isospectral and non-isospectral
flows. Our method can be generalized to other systems to construct symmetries
for non-isospectral equations.


title:
The B-quadrilateral lattice, its transformations and the
  algebro-geometric construction

abstract:
  The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's
discrete BKP equation within the quadrialteral lattice (QL) theory. After
discussing the projective-geometric properties of the lattice we give the
algebro-geometric construction of the BQL ephasizing the role of Prym varieties
and the corresponding theta functions. We also present the reduction of the
vectorial fundamental transformation of the QL to the BQL case.


title: Signature of directed chaos in the conductance of a nanowire

abstract:
  We study the conductance of chaotic or disordered wires in a situation where
equilibrium transport decomposes into biased diffusion and a counter-moving
regular current. A possible realization is a semiconductor nanostructure with
transversal magnetic field and suitably patterned surfaces. We find a
non-trivial dependence of the conductance on the wire length which differs
qualitatively from Ohm's law by the existence of a characteristic length scale
and a finite saturation value.


title:
Experimental and Theoretical Investigations of Stochastic Oscillatory
  Phenomena in a Nonrelativistic Electron Beam with a Virtual Cathode

abstract:
  Results are presented from experimental investigations of oscillatory
phenomena in an electron beam with a virtual cathode in a diode gap with a
decelerating field. Experiments have revealed a stochastic broadband generation
of the microwave oscillations of a virtual cathode in a decelerating field.
Numerical simulations based on a simple one-dimensional model have shown that
the onset of the stochastic generation and the broadening of the oscillation
spectrum with increasing beam deceleration rate are governed by the processes
of regrouping of the electrons in a beam with a virtual cathode.


title:
Adaptive Wavelets Applied to the Analysis of Nonlinear Systems with
  Chaotic Dynamics

abstract:
  We consider an approach to the analysis of nonstationary processes based on
the application of wavelet basis sets constructed using segments of the
analyzed time series. The proposed method is applied to the analysis of time
series generated by a nonlinear system with and without noise


title:
Generalized models as a universal approach to the analysis of nonlinear
  dynamical systems

abstract:
  We present a universal approach to the investigation of the dynamics in
generalized models. In these models the processes that are taken into account
are not restricted to specific functional forms. Therefore a single generalized
models can describe a class of systems which share a similar structure. Despite
this generality, the proposed approach allows us to study the dynamical
properties of generalized models efficiently in the framework of local
bifurcation theory. The approach is based on a normalization procedure that is
used to identify natural parameters of the system. The Jacobian in a steady
state is then derived as a function of these parameters. The analytical
computation of local bifurcations using computer algebra reveals conditions for
the local asymptotic stability of steady states and provides certain insights
on the global dynamics of the system. The proposed approach yields a close
connection between modelling and nonlinear dynamics. We illustrate the
investigation of generalized models by considering examples from three
different disciplines of science: a socio-economic model of dynastic cycles in
china, a model for a coupled laser system and a general ecological food web.


title: Ultra-short solitons and kinetic effects in nonlinear metamaterials

abstract:
  We present a stability analysis of a modified nonlinear Schroedinger equation
describing the propagation of ultra-short pulses in negative refractive index
media. Moreover, using methods of quantum statistics, we derive a kinetic
equation for the pulses, making it possible to analyze and describe partial
coherence in metamaterials. It is shown that a novel short pulse soliton, which
is found analytically, can propagate in the medium.


title: Radial Loewner equation and dispersionless cmKP hierarchy

abstract:
  It has been shown that the dispersionless KP hierarchy (or the Benney
hierarchy) is reduced to the chordal L\"owner equation. We show that the radial
L\"owner equation also gives reduction of a dispersionless type integrable
system. The resulting system acquires another degree of freedom and becomes the
dcmKP hierarchy, which is a ``half'' of the dispersionless Toda hierarchy. The
results of this article was announced in nlin.SI/0512008.


title:
Modelling of radiation defects evolution in regular structures by the
  cellular automata method

abstract:
  The results of modeling of radiation defects formation and evolution on the
surface and in the volume of a crystal are presented in this article.
Statistical properties are calculated for the investigated system. It is
revealed that defects structure is a multifractal and system entropy decreases,
while observing self-organization of the physical system.


title:
Multiresolution analysis of fluctuations in non-stationary time series
  through discrete wavelets

abstract:
  We illustrate the efficacy of a discrete wavelet based approach to
characterize fluctuations in non-stationary time series. The present approach
complements the multi-fractal detrended fluctuation analysis (MF-DFA) method
and is quite accurate for small size data sets. As compared to polynomial fits
in the MF-DFA, a single Daubechies wavelet is used here for de-trending
purposes. The natural, built-in variable window size in wavelet transforms
makes this procedure well suited for non-stationary data. We illustrate the
working of this method through the analysis of binomial multi-fractal model.
For this model, our results compare well with those calculated analytically and
obtained numerically through MF-DFA. To show the efficacy of this approach for
finite data sets, we also do the above comparison for Gaussian white noise time
series of different size. In addition, we analyze time series of three
experimental data sets of tokamak plasma and also spin density fluctuations in
2D Ising model.


title: Extended Camassa-Holm Hierarchy and Conserved Quantities

abstract:
  An extension of the Camassa-Holm hierarchy is constructed in this letter. The
conserved quantities of the hierarchy are studied and a recurrent formula for
the integrals of motion is derived.


title: Behavior of Dynamical Systems in the Regime of Transient Chaos

abstract:
  The transient chaos regime in a two-dimensional system with discrete time
(Eno map) is considered. It is demonstrated that a time series corresponding to
this regime differs from a chaotic series constructed for close values of the
control parameters by the presence of "nonregular" regions, the number of which
increases with the critical parameter. A possible mechanism of this effect is
discussed.


title:
Variation of the Dependence of the Transient Process Duration on the
  Initial Conditions in Systems with Discrete Time

abstract:
  Dependence of the transient process duration on the initial conditions is
considered in one- and two-dimensional systems with discrete time, representing
a logistic map and the Eno map, respectively.


title: Dynamical symmetries for superintegrable quantum systems

abstract:
  We study the dynamical symmetries of a class of two-dimensional
superintegrable systems on a 2-sphere, obtained by a procedure based on the
Marsden-Weinstein reduction, by considering its shape-invariant intertwining
operators. These are obtained by generalizing the techniques of factorization
of one-dimensional systems. We firstly obtain a pair of noncommuting Lie
algebras $su(2)$ that originate the algebra $so(4)$. By considering three
spherical coordinate systems we get the algebra $u(3)$ that can be enlarged by
`reflexions' to $so(6)$. The bounded eigenstates of the Hamiltonian hierarchies
are associated to the irreducible unitary representations of these dynamical
algebras.


title: Analysis of Transient Processes in a Radiophysical Flow System

abstract:
  Transient processes in a third-order radiophysical flow system are studied
and a map of the transient process duration versus initial conditions is
constructed and analyzed. The results are compared to the arrangement of
submanifolds of the stable and unstable cycles in the Poincare section of the
system studied.


title:
A Method for Determining the Transient Process Duration in Dynamic
  Systems in the Regime of Chaotic Oscillations

abstract:
  We describe a method for determining the transient process duration in a
standard two-dimensionaldynamic system with discrete time (Henon map),
occurring in the regime of chaotic oscillations


title:
The Time of Synchronization of Oscillationsin Two Coupled Identical
  Subsystems

abstract:
  The mechanism of synchronization of oscillations in two identical coupled
flow systems has beenstudied. The time (past the coupling onset) during which a
synchronous oscillation regime is establisheddepends on the oscillation phase
difference between the subsystems. Variation of the coupling parameter leadsto
a change in the character of dependence of the synchronization time on the
phase difference. Several typesof synchronization processes are revealed, which
are realized for various values of the coupling parameter.


title:
Duration of the Process of Complete Synchronizationof Two Coupled
  Identical Chaotic Systems

abstract:
  We consider the time required for complete synchronization of two identical
one-way coupled vander Pol-Duffing oscillators occurring in the regime of
dynamic chaos. The influence of the initial phase differ-ence between
oscillators on the duration of the process of complete synchronization has been
studied. At a fixedphase of chaotic oscillations of the self-excited drive
oscillator, the period of time (past the coupling onset) during which the
complete synchronization regime is established depends on the phase of the
self-excited responseoscillator


title: Difference in nature of correlation between NASDAQ and BSE indices

abstract:
  We apply a recently developed wavelet based approach to characterize the
correlation and scaling properties of non-stationary financial time series.
This approach is local in nature and it makes use of wavelets from the
Daubechies family for detrending purpose. The built-in variable windows in
wavelet transform makes this procedure well suited for the non-stationary data.
We analyze daily price of NASDAQ composite index for a period of 20 years, and
BSE sensex index, over a period of 15 years. It is found that the long-range
correlation, as well as fractal behavior for both the stock index values differ
from each other significantly. Strong non-statistical long-range correlation is
observed in BSE index, whose removal revealed a Gaussian random noise character
for the corresponding fluctuation. The NASDAQ index, on the other hand, showed
a multifractal behavior with long-range statistical correlation.


title:
On the Virasoro Structure of Symmetry Algebras of Nonlinear Partial
  Differential Equations

abstract:
  We discuss Lie algebras of the Lie symmetry groups of two generically
non-integrable equations in one temporal and two space dimensions arising in
different contexts. The first is a generalization of the KP equation and
contains 9 arbitrary functions of one and two arguments. The second one is a
system of PDEs that depend on some physical parameters. We require that these
PDEs are invariant under a Kac-Moody-Virasoro algebra. This leads to several
limitations on the coefficients (either functions or parameters) under which
equations are prime candidates for being integrable.


title: On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence

abstract:
  We propose a new approach to the old-standing problem of the anomaly of the
scaling exponents of nonlinear models of turbulence. We achieve this by
constructing, for any given nonlinear model, a linear model of passive
advection of an auxiliary field whose anomalous scaling exponents are the same
as the scaling exponents of the nonlinear problem. The statistics of the
auxiliary linear model are dominated by `Statistically Preserved Structures'
which are associated with exact conservation laws. The latter can be used for
example to determine the value of the anomalous scaling exponent of the second
order structure function. The approach is equally applicable to shell models
and to the Navier-Stokes equations.


title: On the algebraic Bethe ansatz: Periodic boundary conditions

abstract:
  In this paper, the algebraic Bethe ansatz with periodic boundary conditions
is used to investigate trigonometric vertex models associated with the
fundamental representations of the non-exceptional Lie algebras. This
formulation allow us to present explicit expressions for the eigenvectors and
eigenvalues of the respective transfer matrices.


title: Optical ratchets with discrete cavity solitons

abstract:
  We propose a setup to observe soliton ratchet effects using discrete cavity
solitons in a one-dimensional array of coupled waveguide optical resonators.
The net motion of solitons can be generated by an adiabatic shaking of the
holding beam with zero average inclination angle. The resulting soliton
velocity can be controlled by different parameters of the holding beam.


title: Nonlinear dynamics of the viscoelastic Kolmogorov flow

abstract:
  The weakly nonlinear regime of a viscoelastic Navier--Stokes fluid is
investigated. For the purely hydrodynamic case, it is known that large-scale
perturbations tend to the minima of a Ginzburg-Landau free-energy functional
with a double-well (fourth-order) potential. The dynamics of the relaxation
process is ruled by a one-dimensional Cahn--Hilliard equation that dictates the
hyperbolic tangent profiles of kink-antikink structures and their mutual
interactions. For the viscoelastic case, we found that the dynamics still
admits a formulation in terms of a Ginzburg--Landau free-energy functional. For
sufficiently small elasticities, the phenomenology is very similar to the
purely hydrodynamic case: the free-energy functional is still a fourth-order
potential and slightly perturbed kink-antikink structures hold. For
sufficiently large elasticities, a critical point sets in: the fourth-order
term changes sign and the next-order nonlinearity must be taken into account.
Despite the double-well structure of the potential, the one-dimensional nature
of the problem makes the dynamics sensitive to the details of the potential. We
analysed the interactions among these generalized kink-antikink structures,
demonstrating their role in a new, elastic instability. Finally, consequences
for the problem of polymer drag reduction are presented.


title:
Explosive growth of inhomogeneities in the distribution of droplets in a
  turbulent air

abstract:
  We study how the spatial distribution of inertial particles evolves with time
in a random flow. We describe an explosive appearance of caustics and show how
they influence an exponential growth of clusters due to smooth parts of the
flow, leading in particular to an exponential growth of the average distance
between particles.


title: Singularity confinement for maps with the Laurent property

abstract:
  The singularity confinement test is very useful for isolating integrable
cases of discrete-time dynamical systems, but it does not provide a sufficient
criterion for integrability. Quite recently a new property of the bilinear
equations appearing in discrete soliton theory has been noticed: the iterates
of such equations are Laurent polynomials in the initial data. A large class of
non-integrable mappings of the plane are presented which both possess this
Laurent property and have confined singularities.


title:
Mesoscopic modeling of a two-phase flow in the presence of boundaries:
  the Contact Angle

abstract:
  We present a mesoscopic model, based on the Boltzmann Equation, for the
interaction between a solid wall and a non-ideal fluid. We present an analytic
derivation of the contact angle in terms of the surface tension between the
liquid-gas, the liquid-solid and the gas-solid phases. We study the dependency
of the contact angle on the two free parameters of the model, which determine
the interaction between the fluid and the boundaries, i.e. the equivalent of
the wall density and of the wall-fluid potential in Molecular Dynamics studies.
  We compare the analytical results obtained in the hydrodynamical limit for
the density profile and for the surface tension expression with the numerical
simulations. We compare also our two-phase approach with some exact results for
a pure hydrodynamical incompressible fluid based on Navier-Stokes equations
with boundary conditions made up of alternating slip and no-slip strips.
Finally, we show how to overcome some theoretical limitations connected with a
discretized Boltzmann scheme and we discuss the equivalence between the surface
tension defined in terms of the mechanical equilibrium and in terms of the
Maxwell construction.


title: Non-equilibrium ribbon model of scroll waves with twist

abstract:
  We formulate a reduced model to analyze the motion of the core of a twisted
scroll wave. The model is first shown to provide a simple description of the
onset and nonlinear evolution of the helical state appearing in the sproing
bifurcation of scroll waves. It then serves to examine the experimentally
studied case of a medium with spatially-varying excitability. The model shows
the role of sproing in this more complex setting and highlights the differences
between the convective and absolute sproing instabilities.


title: Eigenvectors of open Bazhanov-Stroganov quantum chain

abstract:
  In this contribution we give an explicit formula for the eigenvectors of
Hamiltonians of open Bazhanov-Stroganov quantum chain. The Hamiltonians of this
quantum chain is defined by the generation polynomial $A_n(\lambda)$ which is
upper-left matrix element of monodromy matrix built from the cyclic
$L$-operators. The formulas for the eigenvectors are derived using iterative
procedure by Kharchev and Lebedev and given in terms of $w_p(s)$-function which
is a root of unity analogue of $\Gamma_q$-function.

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


title:
Reproducibility of a noisy limit-cycle oscillator induced by a
  fluctuating input

abstract:
  Reproducibility of a noisy limit-cycle oscillator driven by a random
piecewise constant signal is analyzed. By reducing the model to random phase
maps, it is shown that the reproducibility of the limit cycle generally
improves when the phase maps are monotonically increasing.


title:
Non-Boussinesq Convection at Low Prandtl Numbers: Hexagons and Spiral
  Defect Chaos

abstract:
  We study the stability and dynamics of non-Boussinesq convection in pure
gases (CO$_2$ and SF$_6$) with Prandtl numbers near $Pr\simeq 1$ and in a
H$_2$-Xe mixture with $Pr=0.17$. Focusing on the strongly nonlinear regime we
employ Galerkin stability analyses and direct numerical simulations of the
Navier-Stokes equations. For $Pr \simeq 1$ and intermediate non-Boussinesq
effects we find reentrance of stable hexagons as the Rayleigh number is
increased. For stronger non-Boussinesq effects the hexagons do not exhibit any
amplitude instability to rolls. Seemingly, this result contradicts the
experimentally observed transition from hexagons to rolls. We resolve this
discrepancy by including the effect of the lateral walls. Non-Boussinesq
effects modify the spiral defect chaos observed for larger Rayleigh numbers.
For convection in SF$_6$ we find that non-Boussinesq effects strongly increase
the number of small, compact convection cells and with it enhance the cellular
character of the patterns. In H$_2$-Xe, closer to threshold, we find instead an
enhanced tendency toward roll-like structures. In both cases the number of
spirals and of target-like components is reduced. We quantify these effects
using recently developed diagnostics of the geometric properties of the
patterns.


title: Absorbing processes in Richardson diffusion: analytical results

abstract:
  We consider the recently addressed problem of a passive particle (a
predator), being the center of a ``sphere of interception'' of radius $R$ and
able to absorb other passive particles (the preys) entering into the sphere.
Assuming that all the particles are advected by a turbulent flow and that, in
particular, the Richardson equation properly describes the relative dispersion,
we calculate an analytical expression for the flux into the sphere as a
function of time, assuming an initial constant density of preys outside the
sphere. In the same framework, we show that the distribution of times of first
passage into the sphere has a $t^{-5/2}$ power law tail, seen in contrast to
the $t^{-3/2}$ appearing in standard 3D diffusion. We also discuss the
correction due to the integral length scale on the results in the stationary
case.


title: Nontwist non-Hamiltonian systems

abstract:
  We show that the nontwist phenomena previously observed in Hamiltonian
systems exist also in time-reversible non-Hamiltonian systems. In particular,
we study the two standard collision/reconnection scenarios and we compute the
parameter space breakup diagram of the shearless torus. Besides the Hamiltonian
routes, the breakup may occur due to the onset of attractors. We study these
phenomena in coupled phase oscillators and in non-area-preserving maps.


title:
Periodic wave solutions of nonlinear equations by Hirota's bilinear
  method

abstract:
  In this paper, we use Hirota's bilinear method to directly construct periodic
wave solutions of nonlinear equations.
  The asymptotic property of periodic wave solutions are analyzed. It is shown
that well-known soliton solutions can be reduced from the periodic wave
solutions.


title:
Dynamics of two-dimensional coherent structures in nonlocal nonlinear
  media

abstract:
  We study stability and dynamics of the single cylindrically symmetric
solitary structures and dipolar solitonic molecules in spatially nonlocal
media. The main properties of the solitons, vortex solitons, and dipolar
solitons are investigated analytically and numerically. The vortices and
higher-order solitons show the transverse symmetry-breaking azimuthal
instability below some critical power.
  We find the threshold of the vortex soliton stabilization using the linear
stability analysis and direct numerical simulations. The higher-order solitons,
which have a central peak and one or more surrounding rings, are also
demonstrated to be stabilized in nonlocal nonlinear media. Using direct
numerical simulations, we find a class of radially asymmetric, dipole-like
solitons and show that, at sufficiently high power, these structures are
stable.


title: Conformal invariance in two-dimensional turbulence

abstract:
  Simplicity of fundamental physical laws manifests itself in fundamental
symmetries. While systems with an infinity of strongly interacting degrees of
freedom (in particle physics and critical phenomena) are hard to describe, they
often demonstrate symmetries, in particular scale invariance. In two dimensions
(2d) locality often promotes scale invariance to a wider class of conformal
transformations which allow for nonuniform re-scaling. Conformal invariance
allows a thorough classification of universality classes of critical phenomena
in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example
of strongly-interacting non-equilibrium system? Here, using numerical
experiment, we show that some features of 2d inverse turbulent cascade display
conformal invariance. We observe that the statistics of vorticity clusters is
remarkably close to that of critical percolation, one of the simplest
universality classes of critical phenomena. These results represent a new step
in the unification of 2d physics within the framework of conformal symmetry.


title: Chaotic Sequences for Secure CDMA

abstract:
  One family each of repetitive and non-repetitive spreading sequences for
secure Direct Sequence Spread Spectrum communication are obtained from the
logistic map. The repetitive sequences are perfectly balanced and are found to
have sufficient linear complexity. Applicability of both the families to CDMA
communication is studied by examining their cross-correlation performance. The
cross-correlation is found to be comparable to and only rarely worse than that
of Gold sequences.


title:
Econophysical Dynamics of Market-Based Electric Power Distribution
  Systems

abstract:
  As energy markets begin clearing at sub-hourly rates, their interaction with
load control systems becomes a potentially important consideration. A simple
model for the control of thermal systems using market-based power distribution
strategies is proposed, with particular attention to the behavior and dynamics
of electric building loads and distribution-level power markets. Observations
of dynamic behavior of simple numerical model are compared to that of an
aggregate continuous model. The analytic solution of the continuous model
suggests important deficiencies in each. The continuous model provides very
valuable insights into how one might design such load control system and design
the power markets they interact with. We also highlight important shortcomings
of the continuous model which we believe must be addressed using discrete
models.


title:
Directed transport and Floquet analysis for a periodically kicked
  wavepacket at a quantum resonance

abstract:
  The dynamics of a kicked quantum mechanical wavepacket at a quantum resonance
is studied in the framework of Floquet analysis. It is seen how a directed
current can be created out of a homogeneous initial state at certain resonances
in an asymmetric potential. The almost periodic parameter dependence of the
current is found to be connected with level crossings in the Floquet spectrum.


title: Synchronization of Coupled Nonidentical Genetic Oscillators

abstract:
  The study on the collective dynamics of synchronization among genetic
oscillators is essential for the understanding of the rhythmic phenomena of
living organisms at both molecular and cellular levels. Genetic oscillators are
biochemical networks, which can generally be modelled as nonlinear dynamic
systems. We show in this paper that many genetic oscillators can be transformed
into Lur'e form by exploiting the special structure of biological systems. By
using control theory approach, we provide a theoretical method for analyzing
the synchronization of coupled nonidentical genetic oscillators. Sufficient
conditions for the synchronization as well as the estimation of the bound of
the synchronization error are also obtained. To demonstrate the effectiveness
of our theoretical results, a population of genetic oscillators based on the
Goodwin model are adopted as numerical examples.


title:
Are generalized synchronization and noise--induced synchronization
  identical types of synchronous behavior of chaotic oscillators?

abstract:
  This paper deals with two types of synchronous behavior of chaotic
oscillators -- generalized synchronization and noise--induced synchronization.
It has been shown that both these types of synchronization are caused by
similar mechanisms and should be considered as the same type of the chaotic
oscillator behavior. The mechanisms resulting in the generalized
synchronization are mostly similar to ones taking place in the case of the
noise-induced synchronization with biased noise.


title:
Phase-locking of a Nonlinear Optical Cavity via Rocking: Transmuting
  Vortices into Phase Patterns

abstract:
  We report experimental observation of the conversion of a phase-invariant
nonlinear system into a phase-locked one via the mechanism of rocking [G. J. de
Valcarcel and K. Staliunas, Phys. Rev. E 67, 026604 (2003)]. This conversion
results in that vortices of the phase-invariant system are being replaced by
phase patterns such as domain walls. The experiment is carried out on a
photorefractive oscillator in two-wave mixing configuration.A model for the
experimental device is given that reproduces the observed behavior.


title:
Detecting synchronization of self-sustained oscillators by external
  driving with varying frequency

abstract:
  We propose a method for detecting the presence of synchronization of
self-sustained oscillator by external driving with linearly varying frequency.
The method is based on a continuous wavelet transform of the signals of
self-sustained oscillator and external force and allows one to distinguish the
case of true synchronization from the case of spurious synchronization caused
by linear mixing of the signals. We apply the method to driven van der Pol
oscillator and to experimental data of human heart rate variability and
respiration.


title: An Exactly Solvable Case for a Thin Elastic Rod

abstract:
  We present a new exact solution for the twist of an asymmetric thin elastic
rods. The shape of such rods is described by the static Kirchhoff equations. In
the case of constant curvatire and torsion the twist of the asymmetric rod
represents a soliton lattice.


title: Non-invertible transformations and spatiotemporal randomness

abstract:
  We generalize the exact solution to the Bernoulli shift map. Under certain
conditions, the generalized functions can produce unpredictable dynamics. We
use the properties of the generalized functions to show that certain dynamical
systems can generate random dynamics. For instance, the chaotic Chua's circuit
coupled to a circuit with a non-invertible I-V characteristic can generate
unpredictable dynamics. In general, a nonperiodic time-series with truncated
exponential behavior can be converted into unpredictable dynamics using
non-invertible transformations. Using a new theoretical framework for chaos and
randomness, we investigate some classes of coupled map lattices. We show that,
in some cases, these systems can produce completely unpredictable dynamics. In
a similar fashion, we explain why some wellknown spatiotemporal systems have
been found to produce very complex dynamics in numerical simulations. We
discuss real physical systems that can generate random dynamics.


title: Homoclinic Signatures of Dynamical Localization

abstract:
  It is demonstrated that the oscillations in the width of the momentum
distribution of atoms moving in a phase-modulated standing light field, as a
function of the modulation amplitude, are correlated with the variation of the
chaotic layer width in energy of an underlying effective pendulum. The maximum
effect of dynamical localization and the nearly perfect delocalization are
associated with the maxima and minima, respectively, of the chaotic layer
width. It is also demonstrated that kinetic energy is conserved as an almost
adiabatic invariant at the minima of the chaotic layer width, and that the
system is accurately described by delta-kicked rotors at the zeros of the
Bessel functions J_0 and J_1. Numerical calculations of kinetic energy and
Lyapunov exponents confirm all the theoretical predictions.


title: Avoiding Chaos in Wonderland

abstract:
  Wonderland, a compact, integrated economic, demographic and environmental
model is investigated using methods developed for studying critical phenomena.
Simulation results show the parameter space separates into two phases, one of
which contains the property of long term, sustainable development. By employing
information contain in the phase diagram, an optimal strategy involving
pollution taxes is developed as a means of moving a system initially in a
unsustainable region of the phase diagram into a region of sustainability while
ensuring minimal regret with respect to long term economic growth.


title: Fractional Fokker-Planck Equation for Fractal Media

abstract:
  We consider the fractional generalizations of equation that defines the
medium mass. We prove that the fractional integrals can be used to describe the
media with noninteger mass dimensions. Using fractional integrals, we derive
the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski
equation). In this paper fractional Fokker-Planck equation for fractal media is
derived from the fractional Chapman-Kolmogorov equation. Using the Fourier
transform, we get the Fokker-Planck-Zaslavsky equations that have fractional
coordinate derivatives. The Fokker-Planck equation for the fractal media is an
equation with fractional derivatives in the dual space.

categories: nlin.CD cond-mat.mtrl-sci math-ph math.MP physics.class-ph


title:
Bifurcations from stationary to pulsating solitons in the cubic-quintic
  complex Ginzburg-Landau equation

abstract:
  Stationary to pulsating soliton bifurcation analysis of the complex
Ginzburg-Landau equation (CGLE) is presented. The analysis is based on a
reduction from an infinite-dimensional dynamical dissipative system to a
finite-dimensional model. Stationary solitons, with constant amplitude and
width, are associated with fixed points in the model. For the first time,
pulsating solitons are shown to be stable limit cycles in the
finite-dimensional dynamical system. The boundaries between the two types of
solutions are obtained approximately from the reduced model. These boundaries
are reasonably close to those predicted by direct numerical simulations of the
CGLE.