title: Time Dependent Recursion Operators and Symmetries

abstract:
  The recursion operators and symmetries of non-autonomous, (1+1)-dimensional
integrable evolution equations are considered. It has been previously observed
that the symmetries of the integrable evolution equations obtained through
their recursion operators do not satisfy the symmetry equations. There have
been several attempts to resolve this problem. It is shown that in the case of
time dependent evolution equations or time dependent recursion operators,
associativity is lost. Due to this fact such recursion operators need
modifications. A general formula is given for the missing term of the recursion
operators. Apart from the recursion operators a method is introduced to
calculate the correct symmetries. For illustrations several examples of scalar
and coupled system of equations are considered.


title: Stabilized Kuramoto-Sivashinsky system

abstract:
  A model consisting of a mixed Kuramoto - Sivashinsky - KdV equation, linearly
coupled to an extra linear dissipative equation, is proposed. The model applies
to the description of surface waves on multilayered liquid films. The extra
equation makes its possible to stabilize the zero solution in the model,
opening way to the existence of stable solitary pulses (SPs). Treating the
dissipation and instability-generating gain in the model as small
perturbations, we demonstrate that balance between them selects two
steady-state solitons from their continuous family existing in the absence of
the dissipation and gain. The may be stable, provided that the zero solution is
stable. The prediction is completely confirmed by direct simulations. If the
integration domain is not very large, some pulses are stable even when the zero
background is unstable. Stable bound states of two and three pulses are found
too. The work was supported, in a part, by a joint grant from the Israeli
Minsitry of Science and Technology and Japan Society for Promotion of Science.


title:
Secondary instabilities of hexagons: a bifurcation analysis of
  experimentally observed Faraday wave patterns

abstract:
  We examine three experimental observations of Faraday waves generated by
two-frequency forcing, in which a primary hexagonal pattern becomes unstable to
three different superlattice patterns. We use the symmetry-based approach
developed by Tse et al. to analyse the bifurcations involved in creating the
three new patterns. Each of the three examples reveals a different situation
that can arise in the theoretical analysis.


title: Spatial optical solitons in nonlinear photonic crystals

abstract:
  We study spatial optical solitons in a one-dimensional nonlinear photonic
crystal created by an array of thin-film nonlinear waveguides, the so-called
Dirac-comb nonlinear lattice. We analyze modulational instability of the
extended Bloch-wave modes and also investigate the existence and stability of
bright, dark, and ``twisted'' spatially localized modes in such periodic
structures. Additionally, we discuss both similarities and differences of our
general results with the simplified models of nonlinear periodic media
described by the discrete nonlinear Schrodinger equation, derived in the
tight-binding approximation, and the coupled-mode theory, valid for shallow
periodic modulations of the optical refractive index.


title: Competing Populations in Flows with Chaotic Mixing

abstract:
  We investigate the effects of spatial heterogeneity on the coexistence of
competing species in the case when the heterogeneity is dynamically generated
by environmental flows with chaotic mixing properties. We show that one of the
effects of chaotic advection on the passively advected species (such as
phytoplankton, or self-replicating macromolecules) is the possibility of
coexistence of more species than that limited by the number of niches they
occupy. We derive a novel set of dynamical equations for competing populations.

categories: nlin.CD cond-mat.soft nlin.AO physics.bio-ph q-bio


title: Fast instability indicator in few dimensional dynamical systems

abstract:
  Using the tools of Differential Geometry, we define a new <<fast>> chaoticity
indicator, able to detect dynamical instability of trajectories much more
effectively, (i.e. "quickly") than the usual tools, like Lyapunov
Characteristic Numbers (LCN's) or Poincare` Surface of Section. Moreover, at
variance with other "fast" indicators proposed in the Literature, it gives
informations about the asymptotic behaviour of trajectories, though being local
in phase-space. Furthermore, it detects the chaotic or regular nature of
geodesics without any reference to a given perturbation and it allows also to
discriminate between different regimes (and possibly sources) of chaos in
distinct regions of phase-space.

categories: nlin.CD astro-ph cond-mat.stat-mech math-ph math.MP physics.comp-ph


title:
Spectrally stable encapsulated vortices for nonlinear Schroedinger
  equations

abstract:
  A large class of multidimensional nonlinear Schroedinger equations admit
localized nonradial standing wave solutions that carry nonzero intrinsic
angular momentum. Here we provide evidence that certain of these spinning
excitations are spectrally stable. We find such waves for equations in two
space dimensions with focusing-defocusing nonlinearities, such as
cubic-quintic. Spectrally stable waves resemble a vortex (non-localized
solution with asymptotically constant amplitude) cut off at large radius by a
kink layer that exponentially localizes the solution.
  For the evolution equations linearized about a localized spinning wave, we
prove that unstable eigenvalues are zeros of Evans functions for a finite set
of ordinary differential equations. Numerical computations indicate that there
exist spectrally stable standing waves having central vortex of any degree.


title: Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent

abstract:
  Using the Riemann-Hilbert approach, we study the quasi-linear Stokes
phenomenon for the second Painlev\'e equation $y_{xx}=2y^3+xy-\alpha$. The
precise description of the exponentially small jump in the dominant solution
approaching $\alpha/x$ as $|x|\to\infty$ is given. For the asymptotic power
expansion of the dominant solution, the coefficient asymptotics is found.


title:
Dynamics of modal power distribution in a multimode semiconductor laser
  with optical feedback

abstract:
  The dynamics of power distribution between longitudinal modes of a multimode
semiconductor laser subjected to external optical feedback is experimentally
analyzed in the low-frequency fluctuation regime. Power dropouts in the total
light intensity are invariably accompanied by sudden activations of several
longitudinal modes. These activations are seen not to be simultaneous to the
dropouts, but to occur after them. The phenomenon is statistically analysed in
a systematic way, and the corresponding delay is estimated.


title: 'Animal spirits' and expectations in U.S. recession forecasting

abstract:
  A two-variable model is developed to forecast the probability of recession in
the U.S. economy. Like many others, the model uses data a year or more old to
explain movements of a dichotomous dependent variable for recession. The
innovation of the present effort is the introduction of a confidence variable,
which appears to increase the qualitative accuracy and structural stability of
the model in validation testing compared to others.


title: An Epidemic Model on Small-World Networks and Ring Vaccination

abstract:
  A modified version of susceptible-infected-recovered-susceptible (SIRS) model
for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is
defined on small-world networks, and a ring vaccination programme is included.
This model can be a theoretical explanation for the nonlocal interactions in
epidemic spreading. Ring vaccination is capable of eradicating FMD provided
that the probability of infection is high enough. Also an analytical
approximation for this model is studied.


title: Consolidating boundary methods for finding the eigenstates of billiards

abstract:
  The plane-wave decomposition method (PWDM), a widely used means of
numerically finding eigenstates of the Helmholtz equation in billiard systems
is described as a variant of the mathematically well-established boundary
integral method (BIM). A new unified framework encompassing the two methods is
discussed. Furthermore, a third numerical method, which we call the Gauge
Freedom Method (GFM) is derived from the BIM equations. This opens the way to
further improvements in eigenstate search techniques.


title: Deformations of bihamiltonian structures of hydrodynamic type

abstract:
  In this paper we study the deformations of bihamiltonian PDEs of hydrodynamic
type with one dependent variable. The reason we study such deformations is that
the deformed systems maintain an infinite number of commuting integrals of
motion up to a certain order in the deformation parameter. This fact suggests
that these systems could have, at least for small times, multi-solitons
solutions. Our numerical experiments confirm this hypothesis.


title:
Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic
  Systems

abstract:
  The sensitivity of a wave field's evolution to small perturbations is of
fundamental interest. For chaotic systems, there are two distinct regimes of
either exponential or Gaussian overlap decay in time. We develop a
semiclassical approach for understanding both regimes, and give a simple
expression for the crossover time between the regimes. The wave field's
evolution is considerably more stable than the exponential instability of
chaotic trajectories seem to suggest. The resolution of this paradox lies in
the collective behavior of the appropriate set of trajectories. Results are
given for the standard map.


title: Hyper-complex four-manifolds from the Tzitz\'eica equation

abstract:
  It is shown how solutions to the Tzitz\'eica equation can be used to
construct a family of (pseudo) hyper-complex metrics in four dimensions.


title: A Hamiltonian Flows Associated with Two Dimensional Map

abstract:
  For a given differentiable map $(x,y)\to (X(x,y),Y(x,y))$, which has an
inverse, we show that there exists a Hamiltonian flow in which x plays the role
of the time variable while y is fixed.


title: A Characterization of Discrete Time Soliton Equations

abstract:
  We propose a method to characterize discrete time evolution equations, which
generalize discrete time soliton equations, including the $q$-difference
Painlev\'e IV equations discussed recently by Kajiwara, Noumi and Yamada.


title:
Self-localization of laser induced tumor coagulation limited by heat
  diffusion through active tissue

abstract:
  We analyze the necrosis growth due to thermal coagulation induced by laser
light absorption and limited by heat diffusion into the surrounding live
tissue. The tissue is assumed to contain a certain tumor in the undamaged
tissue whereof the blood perfusion rate does not change during the action. By
contrast, the normal tissue responds strongly to increase in the tissue
temperature and the blood perfusion rate can grow by tenfold. We study in
detail the necrosis formation under conditions typical for a real course of
thermal therapy treatment, the duration of the action is taken about 5 minutes
when a necrosis domain of size about or above 1 cm is formed. In particular, if
the tumor size is sufficiently large, it exceeds 1 cm, and the tissue response
is not too delayed, the delay time does not exceed 1 min, then there are
conditions under which the relative volume of the damaged normal tissue is
small in comparison with the tumor volume after the tumor is coagulated
totally.


title: Properties of Supersymmetric Integrable Systems of KP Type

abstract:
  The recently proposed supersymmetric extensions of reduced
Kadomtsev-Petviashvili (KP) integrable hierarchies in $N =1,2$ superspace are
shown to contain in the purely bosonic limit new types of ordinary
non-supersymmetric integrable systems. The latter are coupled systems of
several multi-component non-linear Schr{\"o}dinger-like hierarchies whose basic
nonlinear evolution equations contain additional quintic and higher-derivative
nonlinear terms. Also, we obtain the N=2 supersymmetric extension of Toda chain
model as Darboux-B{\"a}cklund orbit of the simplest reduced N=2 super-KP
hierarchy and find its explicit solution.


title: Forecasting Portfolio Risk in Normal and Stressed Markets

abstract:
  The instability of historical risk factor correlations renders their use in
estimating portfolio risk extremely questionable. In periods of market stress
correlations of risk factors have a tendency to quickly go well beyond
estimated values. For instance, in times of severe market stress, one would
expect with certainty to see the correlation of yield levels and credit spreads
go to -1, even though historical estimates will miss this region of
correlation. This event might lead to realized portfolio risk profile
substantially different from what was initially estimated. The purpose of this
paper is to explore the correlation driven effects on fixed income portfolio
risks. To achieve this, we propose a methodology to estimate portfolio risks in
both normal and stressed times using confidence weighted forecast correlations.


title: Radiative transport limit for the random Schr\"odinger equation

abstract:
  We give a detailed mathematical analysis of the radiative transport limit for
the average phase space density of solutions of the Schroedinger equation with
time dependent random potential. Our derivation is based on the construction of
an approximate martingale for the random Wigner distribution.


title: The Approach to Ergodicity in the Quantum Baker's Map

abstract:
  We study the quantum mechanics of a generalized version of the baker's map.
We show that the Ruelle resonances (which govern the approach to ergodicity of
classical distributions on phase space) also appear in the quantum correlation
functions of observables at different times, and hence control the statistical
variance of matrix elements of observables (in the basis of eigenstates of the
quantum time evolution operator). We illustrate this with numerical results.


title: Jigsaw model of the origin of life

abstract:
  It is suggested that life originated in a three-step process referred to as
the jigsaw model. RNA, proteins, or similar organic molecules polymerized in a
dehydrated carbon-rich environment, on surfaces in a carbon-rich environment,
or in another environment where polymerization occurs. These polymers
subsequently entered an aqueous environment where they folded into compact
structures. It is argued that the folding of randomly generated polymers such
as RNA or proteins in water tends to partition the folded polymer into domains
with hydrophobic cores and matching shapes to minimize energy. In the aqueous
environment, hydrolysis or other reactions fragmented the compact structures
into two or more matching molecules, occasionally producing simple living
systems, also known as autocatalytic sets of molecules. It is argued that the
hydrolysis of folded polymers such as RNA or proteins is not random. The
hydrophobic cores of the domains are rarely bisected due to the energy
requirements in water. Hydrolysis preferentially fragments the folded polymers
into pieces with complementary structures and chemical affinities. Thus the
probability of producing a system of matched, interacting molecules in
prebiotic chemistry is much higher than usually estimated. Environments where
this process may occur are identified. For example, the jigsaw model suggests
life may have originated at a seep of carbonaceous fluids beneath the ocean.
The polymerization occurred beneath the sea floor. The folding and
fragmentation occurred in the ocean. The implications of this hypothesis for
seeking life or prebiotic chemistry in the Solar System are explored.


title:
The homogeneous balance method, Lax pair, Hirota transformation and a
  general fifth-order KdV equation

abstract:
  In this paper, some notes of the homogeneous balance (HB) method are
discussed by a kind of general fifth-order KdV (fKdV) equation. Frist, the
auto-B\"acklund transformation and lax represents of the higher-order KdV
equation(a specific forms of fKdV equation) are obtained by the HB method.
Then, the connection of the Hirota transformation and the HB method is
discussed by two specific fKdV equations: the Sawada-Kotera equation and the
Lax's equation. At the same time, the solitary wave solution of the general
fifth-order KdV equation is obtained.


title: Complex version KdV equation and the periods solution

abstract:
  In this paper, the complex version KdV equation is discussed. The
corresponding coupled equations is a integrable system in the sense of the
bi-Hamiltonian structure, so the complex version KdV equation is integrable. A
new spectral form is given, the periodic solution of the complex version KdV
equation is obtained. It is showed that the periodic solution is the classical
solution.


title: \QTR{group}{Exact solutions of nonlinear equations}

abstract:
  Based the homogeneous balance method, a general method is suggested to obtain
several kinds of exact solutions for some kinds of nonlinear equations. The
validity and reliability of the method are tested by applying it to the
Bousseneq equation.


title:
Exact solutions of nonlinear PDE, nonlinear transformations and
  reduction nonlinear PDE to a quadrature

abstract:
  A method to construct the exact solution of the PDE is presents, which
combines the two kind methods(the nonlinear transformation and RQ(Reduction the
PDE to a Quadrature problem) method).The nonlinear diffusion equation is chosen
to illustrate the method and the exact solutions are obtained.


title:
Singularites in the Bousseneq equation and in the generalized KdV
  equation

abstract:
  In this paper, two kinds of the exact singular solutions are obtained by the
improved homogeneous balance (HB) method and a nonlinear transformation. The
two exact solutions show that special singular wave patterns exists in the
classical model of some nonlinear wave problems.


title: Suppression and Enhancement of Diffusion in Disordered Dynamical Systems

abstract:
  The impact of quenched disorder on deterministic diffusion in chaotic
dynamical systems is studied. As a simple example, we consider piecewise linear
maps on the line. In computer simulations we find a complicated scenario of
multiple suppression and enhancement of normal diffusion under variation of the
perturbation strength. These results are explained by a theoretical argument
showing that the oscillations emerge as a direct consequence of the unperturbed
diffusion coefficient, which is known to be a fractal function of a control
parameter.


title: Semiclassical spatial correlations in chaotic wave functions

abstract:
  We study the spatial autocorrelation of energy eigenfunctions $\psi_n({\bf
q})$ corresponding to classically chaotic systems in the semiclassical regime.
Our analysis is based on the Weyl-Wigner formalism for the spectral average
$C_{\epsilon}({\bf q^{+}},{\bf q^{-}},E)$ of $\psi_n({\bf q}^{+})\psi_n^*({\bf
q}^{-})$, defined as the average over eigenstates within an energy window
$\epsilon$ centered at $E$. In this framework $C_{\epsilon}$ is the Fourier
transform in momentum space of the spectral Wigner function $W({\bf
x},E;\epsilon)$. Our study reveals the chord structure that $C_{\epsilon}$
inherits from the spectral Wigner function showing the interplay between the
size of the spectral average window, and the spatial separation scale. We
discuss under which conditions is it possible to define a local system
independent regime for $C_{\epsilon}$. In doing so, we derive an expression
that bridges the existing formulae in the literature and find expressions for
$C_{\epsilon}({\bf q^{+}}, {\bf q^{-}},E)$ valid for any separation size $|{\bf
q^{+}}-{\bf q^{-}}|$.


title: Self-written waveguides in photopolymerizable resins

abstract:
  We study the optically-induced growth and interaction of self-written
waveguides in a photopolymerizable resin. We investigate experimentally how the
interaction depends on the mutual coherence and relative power of the input
beams, and suggest an improved analytical model that describes the growth of
single self-written waveguides and the main features of their interaction in
photosensitive materials.


title:
From coherent to incoherent hexagonal patterns in semiconductor
  resonators

abstract:
  We find that hexagonal structures forming in semiconductor resonators can
range from coherent patterns to arrangements of loosely bound spatial solitons,
which can be individually switched. Such incoherent arrangements are stabilized
by gradient forces, as evidenced by the stability of hexagonal structures with
single- or multiple-soliton defects. We interpret the experimental observations
by numerical simulations based on a model for a large aperture semiconductor
microresonator.


title: Mean- Field Approximation and Extended Self-Similarity in Turbulence

abstract:
  Recent experimental discovery of extended self-similarity (ESS) was one of
the most interesting developments, enabling precise determination of the
scaling exponents of fully developed turbulence. Here we show that the ESS is
consistent with the Navier-Stokes equations, provided the pressure -gradient
contributions are expressed in terms of velocity differences in the mean field
approximation (Yakhot, Phys.Rev. E{\bf 63}, 026307, (2001)). A sufficient
condition for extended self-similarity in a general dynamical system


title:
The avalanche dynamics in Bak-Sneppen evolution model observed with
  standard distribution width of fitness

abstract: See the updated version arXiv:nlin/0111028.


title:
On the B\"acklund Transformation for the Moyal Korteweg-de Vries
  Hierarchy

abstract:
  We study the B\"acklund symmetry for the Moyal Korteweg-de Vries (KdV)
hierarchy based on the Kuperschmidt-Wilson Theorem associated with second
  Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes
the result of Adler for the ordinary KdV.


title: How Fast Elements can Affect Slow Dynamics

abstract:
  A chain of coupled chaotic elements with different time scales is studied. In
contrast with the adiabatic approximation, we find correlations between faster
and slower elements when the differences in the time scales of the elements lie
within a certain range. For such correlations to occur, three features are
essential: strong correlations among the elements allowing for both
synchronization and desynchronization, bifurcation in the dynamics of the
fastest element by the change of its control parameter, and the cascade
propagation of the bifurcation. The relevance of our results to biological
memory is briefly discussed.


title:
Modeling Vocal Fold Motion with a Continuum Fluid Dynamic Model, I.
  Derivation and Analysis

abstract:
  Vocal fold (VF) motion is fundamental to voice production and diagnosis in
speech and health sciences. The motion is a consequence of air flow interacting
with elastic vocal fold structures. Motivated by existing lumped mass models
and known flow properties, we propose to model the continuous shape of vocal
fold in motion by the two dimensional compressible Navier-Stokes equations
coupled with an elastic damped driven wave equation on the fold cover. In this
paper, instead of pursuing a direct two dimensional numerical simulation, we
derive reduced quasi-one-dimensional model equations by averaging two
dimensional solutions along the flow cross sections. We then analyze the
oscillation modes of the linearized system about a flat fold, and found that
the fold motion goes through a Hopf bifurcation into temporal oscillation if
the flow energy is sufficient to overcome the damping in the fold consistent
with the early models. We also analyze the further reduced system under the
quasi-steady approximation and compare the resulting vocal fold equation in the
small vibration regime with that of the Titze model. Our model shares several
qualitative features with the Titze model yet differs in the specific form of
energy input from the air flow to the fold. Numerical issues and results of the
quasi-one-dimensional model system will be presented in part II (view resulting
web VF animation at http://www.ma.utexas.edu/users/jxin).


title: Domain-size control by global feedback in bistable systems

abstract:
  We study domain structures in bistable systems such as the Ginzburg-Landau
equation. The size of domains can be controlled by a global negative feedback.
The domain-size control is applied for a localized spiral pattern.


title:
Tri-hamiltonian vector fields, spectral curves and separation
  coordinates

abstract:
  We show that for a class of dynamical systems, Hamiltonian with respect to
three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are
provided by the common roots of a set of bivariate polynomials. These
polynomials, which generalise those considered by E. Sklyanin in his
algebro-geometric approach, are obtained from the knowledge of: (i) a common
Casimir function for the two Poisson pencils (P_1 - \lambda P_0) and (P_2 - \mu
P_0); (ii) a suitable set of vector fields, preserving P_0 but transversal to
its symplectic leaves. The frameworks is applied to Lax equations with spectral
parameter, for which not only it unifies the separation techniques of Sklyanin
and of Magri, but also provides a more efficient ``inverse'' procedure not
involving the extraction of roots.


title:
A Lax Pair for the Dynamics of DNA Modeled as a Shearable and Extensible
  Elastic Rod

abstract:
  We introduce a spectral parameter into the geometrically exact Hamiltonian
equations for the elastic rod in a way that creates a Lax pair. This assures
integrability and permits application of the inverse scattering transform
solution method. If the method can be carried through, the solution of the
original problem is recovered by setting the spectral parameter to zero.


title: Gauge Transformations and Weak Lax Equation

abstract:
  We consider several integrable systems from a standpoint of the SL(2,R)
invariant gauge theory. In the Drinfeld-Sokorov gauge, we get a one parameter
family of nonlinear equations from zero curvature conditions. For each value of
the parameter the equation is described by weak Lax equations. It is
transformed to a set of coupled equations which pass the Painlev\'{e} test and
are integrable for any integer values of the parameter. Performing successive
gauge transformations (the Miura transformations) on the system of equations we
obtain a series of nonlinear equations.


title:
Complete Determination of the Spectrum of a Transfer Operator associated
  with Intermittency

abstract:
  It is well established that the physical phenomenon of intermittency can be
investigated via the spectral analysis of a transfer operator associated with
the dynamics of an interval map with indifferent fixed point. We present here
for the first time a complete spectral analysis for an example of such an
intermittent map, the Farey map. We give a simple proof that the transfer
operator is self-adjoint on a suitably defined Hilbert space and show that its
spectrum decomposes into a continuous part (the interval $[0,1]$) and isolated
eigenvalues of finite multiplicity. Using a suitable first-return map, we
present a highly efficient numerical method for the determination of all the
eigenvalues, including the ones embedded in the continuous spectrum.


title:
Second order Lax pairs of nonlinear partial differential equations with
  Schwarz variants

abstract:
  In this paper, we study the possible second order Lax operators for all the
possible (1+1)-dimensional models with Schwarz variants and some special types
of high dimensional models. It is shown that for every (1+1)-dimensional model
and some special types of high dimensional models which possess Schwarz
variants may have a second order Lax pair. The exiplicit Lax pairs for
(1+1)-dimensional Korteweg de Vries equation, Harry Dym equation, Boussinesq
equation, Caudry-Dodd-Gibbon-Sawada-Kortera equation, Kaup-Kupershmidt
equation, Riccati equation, (2+1)-dimensional breaking soliton equation and a
generalized (2+1)-dimensional fifth order equation are given.


title: High dimensional Schwarzian derivatives and Painlev\'e integrable models

abstract:
  Because of all the known integrable models possess Schwarzian forms with
M\"obious transformation invariance, it may be one of the best way to find new
integrable models starting from some suitable M\"obious transformation
invariant equations. In this paper, the truncated Painlev\'e analysis is used
to find high dimensional Schwarzian derivatives. Especially, a three
dimensional Schwarzian derivative is obtained explicitly. The higher
dimensional higher order Schwarzian derivatives which are invariant under the
M\"obious transformations may be expressed by means of the lower dimensional
lower order ones. All the known Schwarzian derivatives can be used to construct
high dimensional Painlev\'e integrable models.


title: Parity and Ruin in a Stochastic Game

abstract:
  We study an elementary two-player card game where in each round players
compare cards and the holder of the smallest card wins. Using the rate
equations approach, we treat the stochastic version of the game in which cards
are drawn randomly. We obtain an exact solution for arbitrary initial
conditions. In general, the game approaches a steady state where the card
densities of the two players are proportional to each other. The leading small
size behavior of the initial card densities determines the corresponding
proportionality constant, while the next correction governs the asymptotic time
dependence. The relaxation towards the steady state exhibits a rich behavior,
e.g., it may be algebraically slow or exponentially fast. Moreover, in ruin
situations where one player eventually wins all cards, the game may even end in
a finite time.


title:
Breathing Current Domains in Globally Coupled Electrochemical Systems: A
  Comparison with a Semiconductor Model

abstract:
  Spatio-temporal bifurcations and complex dynamics in globally coupled
intrinsically bistable electrochemical systems with an S-shaped current-voltage
characteristic under galvanostatic control are studied theoretically on a
one-dimensional domain. The results are compared with the dynamics and the
bifurcation scenarios occurring in a closely related model which describes
pattern formation in semiconductors. Under galvanostatic control both systems
are unstable with respect to the formation of stationary large amplitude
current domains. The current domains as well as the homogeneous steady state
exhibit oscillatory instabilities for slow dynamics of the potential drop
across the double layer, or across the semiconductor device, respectively. The
interplay of the different instabilities leads to complex spatio-temporal
behavior. We find breathing current domains and chaotic spatio-temporal
dynamics in the electrochemical system. Comparing these findings with the
results obtained earlier for the semiconductor system, we outline bifurcation
scenarios leading to complex dynamics in globally coupled bistable systems with
subcritical spatial bifurcations.


title: Duality, Biorthogonal Polynomials and Multi-Matrix Models

abstract:
  The statistical distribution of eigenvalues of pairs of coupled random
matrices can be expressed in terms of integral kernels having a generalized
Christoffel--Darboux form constructed from sequences of biorthogonal
polynomials. For measures involving exponentials of a pair of polynomials V_1,
V_2 in two different variables, these kernels may be expressed in terms of
finite dimensional ``windows'' spanned by finite subsequences having length
equal to the degree of one or the other of the polynomials V_1, V_2. The
vectors formed by such subsequences satisfy "dual pairs" of first order systems
of linear differential equations with polynomial coefficients, having rank
equal to one of the degrees of V_1 or V_2 and degree equal to the other. They
also satisfy recursion relations connecting the consecutive windows, and
deformation equations, determining how they change under variations in the
coefficients of the polynomials V_1 and V_2. Viewed as overdetermined systems
of linear difference-differential-deformation equations, these are shown to be
compatible, and hence to admit simultaneous fundamental systems of solutions.
The main result is the demonstration of a spectral duality property; namely,
that the spectral curves defined by the characteristic equations of the pair of
matrices defining the dual differential systems are equal upon interchange of
eigenvalue and polynomial parameters.


title: Multifractal properties of return time statistics

abstract:
  Fluctuations in the return time statistics of a dynamical system can be
described by a new spectrum of dimensions. Comparison with the usual
multifractal analysis of measures is presented, and difference between the two
corresponding sets of dimensions is established. Theoretical analysis and
numerical examples of dynamical systems in the class of Iterated Functions are
presented.


title:
A list of all integrable 2D homogeneous polynomial potentials with a
  polynomial integral of order at most 4 in the momenta

abstract:
  We searched integrable 2D homogeneous polynomial potential with a polynomial
first integral by using the so-called direct method of searching for first
integrals. We proved that there exist no polynomial first integrals which are
genuinely cubic or quartic in the momenta if the degree of homogeneous
polynomial potentials is greater than 4.


title:
Asymptotics of semiclassical soliton ensembles: rigorous justification
  of the WKB approximation

abstract:
  Rigorous pointwise asymptotics are established for semiclassical soliton
ensembles (SSEs) of the focusing nonlinear Schroedinger equation using
techniques of asymptotic analysis of matrix Riemann-Hilbert problems. The
accumulation of poles in the eigenfunction is handled using a new method in
which the residues are simultaneously interpolated at the poles by two distinct
interpolants. The results justify the WKB approximation for the nonselfadjoint
Zakharov-Shabat operator with real-analytic, bell-shaped, even potentials. The
new technique introduced in this paper is applicable to other problems as well:
(i) it can be used to provide a unified treatment by Riemann-Hilbert methods of
the zero-dispersion limit of the Korteweg-de Vries equation with negative
(soliton generating) initial data as studied by Lax, Levermore, and Venakides,
and (ii) it allows one to compute rigorous strong asymptotics for systems of
discrete orthogonal polynomials.


title: Wave Chaos in Elastodynamic Cavity Scattering

abstract:
  The exact elastodynamic scattering theory is constructed to describe the
spectral properties of two- and more-cylindrical cavity systems, and compared
to an elastodynamic generalization of the semi-classical Gutzwiller unstable
periodic orbits formulas. In contrast to quantum mechanics, complex periodic
orbits associated with the surface Rayleigh waves dominate the low-frequency
spectrum, and already the two-cavity system displays chaotic features.

categories: nlin.CD math-ph math.DS math.MP quant-ph


title:
The nonlinear steepest descent approach to the asymptotics of the second
  Painleve transcendent in the complex domain

abstract:
  The asymptotics of the generic second Painleve transcendent in the complex
domain is found and justified via the direct asymptotic analysis of the
associated Riemann-Hilbert problem based on the Deift-Zhou nonlinear steepest
descent method. The asymptotics is proved of the Boutroux type, i.e. it is
expressed in terms of the elliptic functions. Explicit connection formulae
between the asymptotic phases in the different sectors are obtained as well.


title: Dynamics of the Subsets of Natural Numbers: A Nursery Rhyme of Chaos

abstract:
  We introduce a metric on the set of all subsets of natural numbers which
converts it into a cantor set.On this set endowed with the metric, we introduce
a very simple map which exhibits chaotic behaviour.This simple map is almost
like a nursery rhyme of chaos.


title: Complex Philosophy

abstract:
  We present several philosophical ideas emerging from the studies of complex
systems. We make a brief introduction to the basic concepts of complex systems,
for then defining "abstraction levels". These are useful for representing
regularities in nature. We define absolute being (observer independent,
infinite) and relative being (observer dependent, finite), and notice the
differences between them. We draw issues on relative causality and absolute
causality among abstraction levels. We also make reflections on determinism. We
reject the search for any absolute truth (because of their infinity), and
promote the idea that all comprehensible truths are relative, since they were
created in finite contexts. This leads us to suggest to search the
less-incompleteness of ideas and contexts instead of their truths.


title: Division Algebras and Extended N=2,4,8 SuperKdVs

abstract:
  The first example of an N=8 supersymmetric extension of the KdV equation is
here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It
corresponds to the unique N=8 solution based on a generalized hamiltonian
dynamics with (generalized) Poisson brackets given by the Non-associative N=8
Superconformal Algebra. The complete list of inequivalent classes of
parametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associative
N=8 SCA" is also furnished. Furthermore, a fundamental domain characterizing
the class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" is
given.


title:
Stable localized pulses and zigzag stripes in a two-dimensional
  diffractive-diffusive Ginzburg-Landau equation

abstract:
  We introduce a model of a two-dimensional (2D) optical waveguide with Kerr
nonlinearity, linear and quintic losses, cubic gain, and temporal-domain
filtering. In the general case, temporal dispersion is also included, although
it is not necessary. The model provides for description of a nonlinear planar
waveguide incorporated into a closed optical cavity. It takes the form of a 2D
cubic-quintic Ginzburg-Landau equation with an anisotropy of a novel type: the
equation is diffractive in one direction, and diffusive in the other. By means
of systematic simulations, we demonstrate that the model gives rise to
\emph{stable} fully localized 2D pulses, which are spatiotemporal ``light
bullets'', existing due to the simultaneous balances between diffraction,
dispersion, and Kerr nonlinearity, and between linear and quintic losses and
cubic gain. A stability region of the 2D pulses is identified in the system's
parameter space. Besides that, we also find that the model generates 1D
patterns in the form of simple localized stripes, which may be stable, or may
exhibit an instability transforming them into oblique stripes with zigzags. The
straight and oblique stripes may stably coexist with the 2D pulse, but not with
each other.


title:
Energy transfer in two-dimensional magnetohydrodynamic turbulence:
  formalism and numerical results

abstract:
  The basic entity of nonlinear interaction in Navier-Stokes and the
Magnetohydrodynamic (MHD) equations is a wavenumber triad ({\bf k,p,q})
satisfying ${\bf k+p+q=0}$. The expression for the combined energy transfer
from two of these wavenumbers to the third wavenumber is known. In this paper
we introduce the idea of an effective energy transfer between a pair of modes
by the mediation of the third mode, and find an expression for it. Then we
apply this formalism to compute the energy transfer in the quasi-steady-state
of two-dimensional MHD turbulence with large-scale kinetic forcing. The
computation of energy fluxes and the energy transfer between different
wavenumber shells is done using the data generated by the pseudo-spectral
direct numerical simulation. The picture of energy flux that emerges is quite
complex---there is a forward cascade of magnetic energy, an inverse cascade of
kinetic energy, a flux of energy from the kinetic to the magnetic field, and a
reverse flux which transfers the energy back to the kinetic from the magnetic.
The energy transfer between different wavenumber shells is also complex---local
and nonlocal transfers often possess opposing features, i.e., energy transfer
between some wavenumber shells occurs from kinetic to magnetic, and between
other wavenumber shells this transfer is reversed. The net transfer of energy
is from kinetic to magnetic. The results obtained from the studies of flux and
shell-to-shell energy transfer are consistent with each other.


title: Correlations of chaotic eigenfunctions: a semiclassical analysis

abstract:
  We derive a semiclassical expression for an energy smoothed autocorrelation
function defined on a group of eigenstates of the Schr\"odinger equation. The
system we considered is an energy-conserved Hamiltonian system possessing
time-invariant symmetry. The energy smoothed autocorrelation function is
expressed as a sum of three terms. The first one is analogous to Berry's
conjecture, which is a Bessel function of the zeroth order. The second and the
third terms are trace formulae made from special trajectories. The second term
is found to be direction dependent in the case of spacing averaging, which
agrees qualitatively with previous numerical observations in high-lying
eigenstates of a chaotic billiard.


title: Precision Measurements of Stretching and Compression in Fluid Mixing

abstract:
  The mixing of an impurity into a flowing fluid is an important process in
many areas of science, including geophysical processes, chemical reactors, and
microfluidic devices. In some cases, for example periodic flows, the concepts
of nonlinear dynamics provide a deep theoretical basis for understanding
mixing. Unfortunately, the building blocks of this theory, i.e. the fixed
points and invariant manifolds of the associated Poincare map, have remained
inaccessible to direct experimental study, thus limiting the insight that could
be obtained. Using precision measurements of tracer particle trajectories in a
two-dimensional fluid flow producing chaotic mixing, we directly measure the
time-dependent stretching and compression fields. These quantities, previously
available only numerically, attain local maxima along lines coinciding with the
stable and unstable manifolds, thus revealing the dynamical structures that
control mixing. Contours or level sets of a passive impurity field are found to
be aligned parallel to the lines of large compression (unstable manifolds) at
each instant. This connection appears to persist as the onset of turbulence is
approached.


title:
Lyapunov instability for a periodic Lorentz gas thermostated by
  deterministic scattering

abstract:
  In recent work a deterministic and time-reversible boundary thermostat called
thermostating by deterministic scattering has been introduced for the periodic
Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the
nonlinear properties of this new dynamical system by numerically calculating
its Lyapunov exponents. Based on a revised method for computing Lyapunov
exponents, which employs periodic orthonormalization with a constraint, we
present results for the Lyapunov exponents and related quantities in
equilibrium and nonequilibrium. Finally, we check whether we obtain the same
relations between quantities characterizing the microscopic chaotic dynamics
and quantities characterizing macroscopic transport as obtained for
conventional deterministic and time-reversible bulk thermostats.


title: Analytic solutions for nonlinear waves in coupled reacting systems

abstract:
  We analyze a system of reacting elements harmonically coupled to nearest
neighbors in the continuum limit. An analytic solution is found for traveling
waves. The procedure is used to find oscillatory as well as solitary waves. A
comparison is made between exact solutions and solutions of the piecewise
linearized system, showing how the linearization affects the amplitude and
frequency of the solutions.


title:
Generalized Kadomtsev-Petviashvili equation with an infinite dimensional
  symmetry algebra

abstract:
  A generalized Kadomtsev-Petviashvili equation, describing water waves in
oceans of varying depth, density and vorticity is discussed. A priori, it
involves 9 arbitrary functions of one, or two variables. The conditions are
determined under which the equation allows an infinite dimensional symmetry
algebra. This algebra can involve up to three arbitrary functions of time. It
depends on precisely three such functions if and only if it is completely
integrable.


title: Multicomponent bi-superHamiltonian KdV systems

abstract:
  It is shown that a new class of classical multicomponent super KdV equations
is bi-superHamiltonian by extending the method for the verification of graded
Jacobi identity. The multicomponent extension of super mKdV equations is
obtained by using the super Miura transformation.


title:
Collective motions in globally coupled tent maps with stochastic
  updating

abstract:
  We study a generalization of globally coupled maps, where the elements are
updated with probability $p$. When $p$ is below a threshold $p_c$, the
collective motion vanishes and the system is the stationary state in the large
size limit. We present the linear stability analysis.


title: Phase relaxation of Faraday surface waves

abstract:
  Surface waves on a liquid air interface excited by a vertical vibration of a
fluid layer (Faraday waves) are employed to investigate the phase relaxation of
ideally ordered patterns. By means of a combined frequency-amplitude modulation
of the excitation signal a periodic expansion and dilatation of a square wave
pattern is generated, the dynamics of which is well described by a Debye
relaxator. By comparison with the results of a linear theory it is shown that
this practice allows a precise measurement of the phase diffusion constant.


title:
Stability of spinning ring solitons of the cubic-quintic nonlinear
  Schrodinger equation

abstract:
  We investigate stability of (2+1)-dimensional ring solitons of the nonlinear
Schrodinger equation with focusing cubic and defocusing quintic nonlinearities.
Computing eigenvalues of the linearised equation, we show that rings with spin
(topological charge) s=1 and s=2 are linearly stable, provided that they are
very broad. The stability regions occupy, respectively, 9% and 8% of the
corresponding existence regions. These results finally resolve a controversial
stability issue for this class of models.


title:
Discriminating dynamical from additive noise in the Van der Pol
  oscillator

abstract:
  We address the distinction between dynamical and additive noise in time
series analysis by making a joint evaluation of both the statistical continuity
of the series and the statistical differentiability of the reconstructed
measure. Low levels of the latter and high levels of the former indicate the
presence of dynamical noise only, while low values of the two are observed as
soon as additive noise contaminates the signal. The method is presented through
the example of the Van der Pol oscillator, but is expected to be of general
validity for continuous-time systems.


title: Wealth redistribution with finite resources

abstract:
  We present a simplified model for the exploitation of finite resources by
interacting agents, where each agent receives a random fraction of the
available resources. An extremal dynamics ensures that the poorest agent has a
chance to change its economic welfare. After a long transient, the system
self-organizes into a critical state that maximizes the average performance of
each participant. Our model exhibits a new kind of wealth condensation, where
very few extremely rich agents are stable in time and the rest stays in the
middle class.


title: Tailoring the profile and interactions of optical localized structures

abstract:
  We experimentally demonstrate the broad tunability of the main features of
optical localized structures (LS) in a nonlinear interferometer. By discussing
how a single LS depends on the system spatial frequency bandwidth, we show that
a modification of its tail leads to the possibility of tuning the interactions
between LS pairs, and thus the equilibrium distances at which LS bound states
form. This is in agreement with a general theoretical model describing weak
interactions of LS in nonlinear dissipative systems.


title: Detecting Determinism in High Dimensional Chaotic Systems

abstract:
  A method based upon the statistical evaluation of the differentiability of
the measure along the trajectory is used to identify in high dimensional
systems. The results show that the method is suitable for discriminating
stochastic from deterministic systems even if the dimension of the latter is as
high as 13. The method is shown to succeed in identifying determinism in
electro-encephalogram signals simulated by means of a high dimensional system.


title:
Triggering synchronized oscillations through arbitrarily weak diversity
  in close-to-threshold excitable media

abstract:
  It is shown that arbitrarily weak (frozen) heterogeneity can induce global
synchronized oscillations in excitable media close to threshold. The work is
carried out on networks of coupled van der Pol-FitzHugh-Nagumo oscillators. The
result is shown to be robust against the presence of internal dynamical noise.


title: Olfactory search at high Reynolds number

abstract:
  Locating the source of odor in a turbulent environment - a common behavior
for living organisms - is non-trivial because of the random nature of mixing.
Here we analyze the statistical physics aspects of the problem and propose an
efficient strategy for olfactory search which can work in turbulent plumes. The
algorithm combines the maximum likelihood inference of the source position with
an active search. Our approach provides the theoretical basis for the design of
olfactory robots and the quantitative tools for the analysis of the observed
olfactory search behavior of living creatures (e.g. odor modulated optomotor
anemotaxis of moth)


title: Autonomous Bursting in a Homoclinic System

abstract:
  A continuous train of irregularly spaced spikes, peculiar of homoclinic
chaos, transforms into clusters of regularly spaced spikes, with quiescent
periods in between (bursting regime), by feeding back a low frequency portion
of the dynamical output. Such autonomous bursting results to be extremely
robust against noise; we provide experimental evidence of it in a CO2 laser
with feedback. The phenomen here presented display qualitative analogies with
bursting phenomena in neurons.


title: Delayed Self-Synchronization in Homoclinic Chaos

abstract:
  The chaotic spike train of a homoclinic dynamical system is self-synchronized
by re-inserting a small fraction of the delayed output. Due to the sensitive
nature of the homoclinic chaos to external perturbations, stabilization of very
long periodic orbits is possible. On these orbits, the dynamics appears chaotic
over a finite time, but then it repeats with a recurrence time that is slightly
longer than the delay time. The effect, called delayed self-synchronization
(DSS), displays analogies with neurodynamic events which occur in the build-up
of long term memories.


title:
Data Analysis: Generalizations of the Local Approximation Method by
  Singular Spectrum Analysis

abstract:
  We study forecasting capabilities of the methods of Singular Spectrum
Analysis (SSA) and Local Approximation (LA). A practical implementation of
these methods to several time series is described. Details of the algorithms of
these methods are discussed. Advantages and disadvantages of SSA and LA are
given. On the basis of our results we generalize LA and SSA and propose a new
way for time series forecasting including strongly noisy signals. This allowed
us to extend the range of application of LA in comparison with the known
standard scheme. For the problem of forecasting, the accuracy enhancement of
the numerical computations is discussed.


title:
On the performance of different synchronization measures in real data: a
  case study on EEG signals

abstract:
  We study the synchronization between left and right hemisphere rat EEG
channels by using various synchronization measures, namely non-linear
interdependences, phase-synchronizations, mutual information, cross-correlation
and the coherence function. In passing we show a close relation between two
recently proposed phase synchronization measures and we extend the definition
of one of them. In three typical examples we observe that except mutual
information, all these measures give a useful quantification that is hard to be
guessed beforehand from the raw data. Despite their differences, results are
qualitatively the same. Therefore, we claim that the applied measures are
valuable for the study of synchronization in real data. Moreover, in the
particular case of EEG signals their use as complementary variables could be of
clinical relevance.

categories: nlin.CD cond-mat.dis-nn physics.bio-ph physics.comp-ph physics.data-an physics.med-ph


title:
Describing Rates of Interaction between Multiple Autonomous Entities: An
  Example Using Combat Modelling

abstract:
  This paper endeavors to show how a fractal-based approach can offer an
alternative to differential equations for describing rates of interaction in
complex systems. The specific example given is for combat analysis. This
concerns a scenario of some similarity to the situation in Mogadishu in 1993,
for which military analysts struggled to provide useful analytical tools. It is
seen that the correlated dispositions of the entities in the model lend
themselves to being described by fractal dimensions. This appears to lead to
power laws for the rate of attrition. An equation is suggested to describe this
phenomenon. This is particularly interesting because it is an example of a
power-law dependent on one of the parameters of the model rather than a
temporal or spatial scale.


title:
Reconstructing Bologna. The City as an Emergent Computational System - A
  Study in the Complexity of Urban Structures. Part I: The Basic Idea and
  Fundamental Concepts

abstract:
  The conceptual background for a detailed study of the urban form of the city
of Bologna is discussed with a view to modern methodological insight as it is
being presented by recent results of complexity theory and the theory of
self-organized criticality. The basic idea is to visualize the city of Bologna
as an example of a massively parallely organized and interacting complex
computational system in the sense of these recent theories. It is proposed to
relate aspects of urban evolution to a universal concept of evolution which is
governing all processes in nature. The universality of this approach is thought
of as being an epistemological advantage as compared to more classical studies
utilizing primarily local and specific methods for their modelling procedures.
To actually establish whether this is in fact an advantage or not will be one
of the main results of this present series of papers. In this very first part
of the study, the basic idea is explicated in some detail, and the fundamental
concepts are introduced in order to clarify the terminology utilized in the
following. Two more parts of this study will follow in due time.


title: Information encoding in homoclinic chaotic systems

abstract:
  In this work we describe a simple method of encoding information at real time
in the inter-spike intervals of a homoclinic chaotic system. This has been
experimentally tested by means of an instantaneous synchronization between the
laser intensity of a CO2 laser with feedback in the regime of Sil'nikov chaos
and an external pulsed signal of very low power. The information is previously
encoded in the temporal intervals between consecutive pulses of the external
signal. The value of the inter-pulse intervals is varied each time a new pulse
is generated.


title: Ray dynamics in ocean acoustics

abstract:
  Recent results relating to ray dynamics in ocean acoustics are reviewed.
Attention is focussed on long-range propagation in deep ocean environments. For
this class of problems, the ray equations may be simplified by making use of a
one-way formulation in which the range variable appears as the independent
(time-like) variable. Topics discussed include integrable and non-integrable
ray systems, action-angle variables, nonlinear resonances and the KAM theorem,
ray chaos, Lyapunov exponents, predictability, nondegeneracy violation, ray
intensity statistics, semiclassical breakdown, wave chaos, and the connection
between ray chaos and mode coupling. The Hamiltonian structure of the ray
equations plays an important role in all of these topics.


title: Du chaos dans la musique des etoiles

abstract:
  La plupart des etoiles variables qui pulsent avec grande amplitude, telles
les cepheides, ont un comportement tres regulier et periodique. Mais juste a
cote d'elles dans le diagramme Hertzsprung-Russell, se trouve un groupe
d'etoiles variables dotees de courbes de lumiere tres irregulieres. A l'aide
d'une technique de reconstruction de flot appliquee aux donnees d'observation
astronomiques de plusieurs de ces etoiles, on montre que la dynamique
sous-jacente est chaotique et de faible dimension, ce qui peut surprendre a
cause de la violence de ces pulsations. En plus a l'aide d'une linearisation du
flot on deduit que le mecanisme physique de la pulsation consiste en
l'interaction entre deux modes vibratoires (vraisemblablement radiaux), l'un
lineairement instable, de frequence f_0, et l'autre stable, mais de frequence
\~2f_0 (soit un scenario a la Shilnikoff generalise).

categories: nlin.CD astro-ph physics.ao-ph physics.data-an


title: Nodal domains statistics - a criterion for quantum chaos

abstract:
  We consider the distribution of the (properly normalized) numbers of nodal
domains of wave functions in 2-$d$ quantum billiards. We show that these
distributions distinguish clearly between systems with integrable (separable)
or chaotic underlying classical dynamics, and for each case the limiting
distribution is universal (system independent). Thus, a new criterion for
quantum chaos is provided by the statistics of the wave functions, which
complements the well established criterion based on spectral statistics.


title:
Interaction of N solitons in the massive Thirring model and optical gap
  system: the Complex Toda Chain Model

abstract:
  Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton
interaction I show that the train propagation of N well separated solitons of
the massive Thirring model is described by the complex Toda chain with N nodes.
For the optical gap system a generalised (non-integrable) complex Toda chain is
derived for description of the train propagation of well separated gap
solitons. These results are in favor of the recently proposed conjecture of
universality of the complex Toda chain.


title: Decouple a coupled KdV system of Nutku and O\~{g}uz

abstract:
  A coupled KdV system with a free parameter proposed by Nutku and O\~{g}uz is
considered. It is shown that the system passes the WTC's Painlev\'{e} test for
arbitrary value of the parameter. A further analysis yields that the parameter
can be scaled away and the system can be decoupled.


title: Hydrodynamics of thermal granular convection

abstract:
  A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular
convection, recently predicted in molecular dynamic simulations and observed in
experiment. The limit of a dilute flow is considered. The problem is fully
described by three scaled parameters. The convection occurs via a supercritical
bifurcation, the inelasticity of the collisions being the control parameter.
The theory is expected to be valid for small Knudsen numbers and nearly elastic
grain collisions.


title: Integrable systems on quad-graphs

abstract:
  We consider general integrable systems on graphs as discrete flat connections
with the values in loop groups. We argue that a certain class of graphs is of a
special importance in this respect, namely quad-graphs, the cellular
decompositions of oriented surfaces with all two-cells being quadrilateral. We
establish a relation between integrable systems on quad-graphs and discrete
systems of the Toda type on graphs. We propose a simple and general procedure
for deriving discrete zero curvature representations for integrable systems on
quad-graphs, based on the principle of the three-dimensional consistency. Thus,
finding a zero curvature representation is put on an algorithmic basis and does
not rely on the guesswork anymore. Several examples of integrable systems on
quad-graphs are considered in detail, their geometric interpretation is given
in terms of circle patterns.


title: Periodic orbit quantization of chaotic maps by harmonic inversion

abstract:
  A method for the semiclassical quantization of chaotic maps is proposed,
which is based on harmonic inversion. The power of the technique is
demonstrated for the baker's map as a prototype example of a chaotic map.


title:
Semi-classical calculations of the two-point correlation form factor for
  diffractive systems

abstract:
  The computation of the two-point correlation form factor K(t) is performed
for a rectangular billiard with a small size impurity inside for both periodic
or Dirichlet boundary conditions. It is demonstrated that all terms of
perturbation expansion of this form factor in powers of t can be computed
directly by semiclassical trace formula. The main part of the calculation is
the summation of non-diagonal terms in the cross product of classical orbits.
When the diffraction coefficient is a constant our results coincide with
expansion of exact expressions ontained by a different method.


title: Stable synchronised states of coupled Tchebyscheff maps

abstract:
  Coupled Tchebyscheff maps have recently been introduced to explain parameters
in the standard model of particle physics, using the stochastic quantisation of
Parisi and Wu. This paper studies dynamical properties of these maps, finding
analytic expressions for a number of periodic states and determining their
linear stability. Numerical evidence is given for nonlinear stability of these
states, and also the presence of exponentially slow dynamics for some ranges of
the parameter. These results indicate that a theory of particle physics based
on coupled map lattices must specify strong physical arguments for any choice
of initial conditions, and explain how stochastic quantisation is obtained in
the many stable parameter regions.


title: Network as a Complex System: Information Flow Analysis

abstract:
  A new approach for the analysis of information flow on a network is suggested
using protocol parameters encapsulated in the package headers as functions of
time. The minimal number of independent parameters for a complete description
of the information flow (phase space dimension of the information flow) is
found to be about 10 - 12.


title:
The resonance spectrum of the cusp map in the space of analytic
  functions

abstract:
  We prove that the Frobenius--Perron operator $U$ of the cusp map
$F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the
Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions
corresponding to eigenvalues different from 0 and 1. We also prove that for any
$q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk
$\{z\in\C:|z-q|<1+q\}$ is the union of the segment $[0,1]$ and some finite or
countably infinite set of isolated eigenvalues of finite multiplicity.


title: Markov-chain approach to a process with long-time memory

abstract:
  We show that long-term memory effects, present in the chaotic dispersion
process generated by a meandering jet model, can be nonetheless taken into
account by a first order Markov process, provided that the states of the phase
space partition, chosen to describe the system, be appropriately defined.


title: Front speed enhancement in cellular flows

abstract:
  The problem of front propagation in a stirred medium is addressed in the case
of cellular flows in three different regimes: slow reaction, fast reaction and
geometrical optics limit. It is well known that a consequence of stirring is
the enhancement of front speed with respect to the non-stirred case. By means
of numerical simulations and theoretical arguments we describe the behavior of
front speed as a function of the stirring intensity, $U$. For slow reaction,
the front propagates with a speed proportional to $U^{1/4}$, conversely for
fast reaction the front speed is proportional to $U^{3/4}$. In the geometrical
optics limit, the front speed asymptotically behaves as $U/\ln U$.


title: Kowalevski top revisited

abstract:
  We review the separation of variables for the Kowalevski top and for its
generalization to the algebra o(4). We notice that the corresponding separation
equations allow an interpretation of the Kowalevski top as a B2 integrable
lattice. Consequently, we apply the quadratic r-matrix formalism to construct a
new 2x2 Lax matrix for the top, which is responsible for its separation of
variables.


title: Broken symmetries and directed collective energy transport

abstract:
  We study the appearance of directed energy current in homogeneous spatially
extended systems coupled to a heat bath in the presence of an external ac field
E(t). The systems are described by nonlinear field equations. By making use of
a symmetry analysis we predict the right choice of E(t) and obtain directed
energy transport for systems with a nonzero topological charge Q. We
demonstrate that the symmetry properties of motion of topological solitons
(kinks and antikinks) are equivalent to the ones for the energy current.
Numerical simulations confirm the predictions of the symmetry analysis and,
moreover, show that the directed energy current drastically increases as the
dissipation parameter $\alpha$ reduces. Our results generalize recent rigorous
theories of currents generated by broken time-space symmetries to the case of
interacting many-particle systems.


title: Mechanical Systems with Poincare Invariance

abstract:
  Some years ago Ruijsenaars and Schneider initiated the study of mechanical
systems exhibiting an action of the Poincare algebra. The systems they
discovered were far richer: their models were actually integrable and possessed
a natural quantum version. We follow this early work finding and classifying
mechanical systems with such an action. New solutions are found together with a
new class of models exhibiting an action of the Galilean algebra. These are
related to the functional identities underlying the various Hirzebruch genera.
The quantum mechanics is also discussed.


title: Direction reversing travelling waves in the Fermi-Pasta-Ulam chain

abstract:
  This paper considers the famous Fermi-Pasta-Ulam chain with periodic boundary
conditions and quartic nonlinearities. Due to special resonances and discrete
symmetries, the Birkhoff normal form of this Hamiltonian system is completely
integrable. We study how the level sets of the integrals foliate the phase
space. Our study reveals all the integrable structure in the low energy domain
of the chain. If the number of particles in the chain is even, then this
foliation is singular. The method of singular reduction shows that the system
has invariant pinched tori and monodromy. Monodromy is an obstruction to the
existence of global action-angle variables. The pinched tori are interpreted as
homoclinic and heteroclinic connections between travelling waves. Thus we
discover a new class of solutions which can be described as direction reversing
travelling waves. They remarkably show an interesting interaction of normal
modes in the absense of energy transfer. These solutions can easily be observed
numerically.


title: Scaling and universality in turbulent convection

abstract:
  Anomalous correlation functions of the temperature field in two-dimensional
turbulent convection are shown to be universal with respect to the choice of
external sources. Moreover, they are equal to the anomalous correlations of the
concentration field of a passive tracer advected by the convective flow itself.
The statistics of velocity differences is found to be universal, self-similar
and close to Gaussian. These results point to the conclusion that temperature
intermittency in two-dimensional turbulent convection may be traced back to the
existence of statistically preserved structures, as it is in passive scalar
turbulence.


title: Dynamics of Defects in the Vector Complex Ginzburg-Landau Equation

abstract:
  Coupled Ginzburg-Landau equations appear in a variety of contexts involving
instabilities in oscillatory media. When the relevant unstable mode is of
vectorial character (a common situation in nonlinear optics), the pair of
coupled equations has special symmetries and can be written as a vector complex
Ginzburg-Landau equation. Dynamical properties of localized structures of
topological character in this vector-field case are considered. Creation and
annihilation processes of different kinds of vector defects are described, and
some of them interpreted in theoretical terms. A transition between different
regimes of spatiotemporal dynamics is described.


title: Master Integrals, Superintegrability and Quadratic Algebras

abstract:
  In this paper we use a generalization of Oevel's theorem about master
symmetries to relate them with superintegrability and quadratic algebras.


title: Percolation model for nodal domains of chaotic wave functions

abstract:
  Nodal domains are regions where a function has definite sign. In recent paper
[nlin.CD/0109029] it is conjectured that the distribution of nodal domains for
quantum eigenfunctions of chaotic systems is universal. We propose a
percolation-like model for description of these nodal domains which permits to
calculate all interesting quantities analytically, agrees well with numerical
simulations, and due to the relation to percolation theory opens the way of
deeper understanding of the structure of chaotic wave functions.


title: Stopping Light on a Defect

abstract:
  Gap solitons are localized nonlinear coherent states which have been shown
both theoretically and experimentally to propagate in periodic structures.
Although theory allows for their propagation at any speed $v$, $0\le v\le c$,
they have been observed in experiments at speeds of approximately 50% of $c$.
It is of scientific and technological interest to trap gap solitons. We first
introduce an explicit multiparameter family of periodic structures with
localized defects, which support linear defect modes. These linear defect modes
are shown to persist into the nonlinear regime, as {\it nonlinear defect
modes}. Using mathematical analysis and numerical simulations we then
investigate the capture of an incident gap soliton by these defects. The
mechanism of capture of a gap soliton is resonant transfer of its energy to
nonlinear defect modes. We introduce a useful bifurcation diagram from which
information on the parameter regimes of gap soliton capture, reflection and
transmission can be obtained by simple conservation of energy and resonant
energy transfer principles.


title: A unified treatment of quartic invariants at fixed and arbitrary energy

abstract:
  Two-dimensional Hamiltonian systems admitting second invariants which are
quartic in the momenta are investigated using the Jacobi geometrization of the
dynamics. This approach allows for a unified treatment of invariants at both
arbitrary and fixed energy. In the differential geometric picture, the quartic
invariant corresponds to the existence of a fourth rank Killing tensor.
Expressing the Jacobi metric in terms of a Kahler potential, the integrability
condition for the existence of the Killing tensor at fixed energy is a
non-linear equation involving the Kahler potential. At arbitrary energy,
further conditions must be imposed which lead to an overdetermined system with
isolated solutions. We obtain several new integrable and superintegrable
systems in addition to all previously known examples.


title: Generalized Kowalevski top: new integrable cases on $e(3)$ and $so(4)$

abstract:
  A three-parameter family of integrable quadratic Hamiltonians on $e(3)$ and
$so(4)$ is presented. When one of the parameters vanishes, the Hamiltonian
coincides with the Kowalevski Hamiltonian with the girostatic term. If the
other two parameters are equal to zero then the Hamiltonian reduces to a new
integrable case of the Kirchhoff equations found recently by the author.


title: Transitions from deterministic to stochastic diffusion

abstract:
  We examine characteristic properties of deterministic and stochastic
diffusion in low-dimensional chaotic dynamical systems. As an example, we
consider a periodic array of scatterers defined by a simple chaotic map on the
line. Adding different types of time-dependent noise to this model we compute
the diffusion coefficient from simulations. We find that there is a crossover
from deterministic to stochastic diffusion under variation of the perturbation
strength related to different asymptotic laws for the diffusion coefficient.
Typical signatures of this scenario are suppression and enhancement of normal
diffusion. Our results are explained by a simple theoretical approximation.


title:
Long-Time Asymptotics of Solutions to the Cauchy Problem for the
  Defocusing Non-Linear Schr\"{o}dinger Equation with Finite Density Initial
  Data. I. Solitonless Sector

abstract:
  The methodology of the Riemann-Hilbert (RH) factorisation approach for
Lax-pair isospectral deformations is used to derive, in the solitonless sector,
the leading-order asymptotics as $t \to \pm \infty$ $(x/t \sim \mathcal{O}(1))$
of solutions to the Cauchy problem for the defocusing non-linear
Schr\"{o}dinger equation (D${}_{f}$NLSE), $\mi \partial_{t}u
+\partial_{x}^{2}u-2(| u |^{2}-1)u=0$, with (finite-density) initial data
$u(x,0)=_{x \to \pm \infty} \exp (\tfrac{\mi (1 \mp 1) \theta}{2})(1+ o(1))$,
$\theta \in [0,2 \pi)$. A limiting case of these asymptotics related to the RH
problem for the Painlev\'{e} II equation, or one of its special reductions, is
also identified.


title:
Statically Transformed Autoregressive Process and Surrogate Data Test
  for Nonlinearity

abstract:
  The key feature for the successful implementation of the surrogate data test
for nonlinearity on a scalar time series is the generation of surrogate data
that represent exactly the null hypothesis (statically transformed normal
stochastic process), i.e. they possess the sample autocorrelation and amplitude
distribution of the given data. A new conceptual approach and algorithm for the
generation of surrogate data is proposed, called {\em statically transformed
  autoregressive process} (STAP). It identifies a normal autoregressive process
and a monotonic static transform, so that the transformed realisations of this
process fulfill exactly both conditions and do not suffer from bias in
autocorrelation as the surrogate data generated by other algorithms. The
appropriateness of STAP is demonstrated with simulated and real world data.


title: Soliton ratchets induced by ac forces with harmonic mixing

abstract:
  The ratchet dynamics of a kink (topological soliton) of a dissipative
sine-Gordon equation in the presence of ac forces with harmonic mixing (at
least bi-harmonic) of zero mean is studied. The dependence of the kink mean
velocity on system parameters is investigated numerically and the results are
compared with a perturbation analysis based on a point particle representation
of the soliton. We find that first order perturbative calculations lead to
incomplete descriptions, due to the important role played by the soliton-phonon
interaction in establishing the phenomenon. The role played by the temporal
symmetry of the system in establishing soliton ratchets is also emphasized. In
particular, we show the existence of an asymmetric internal mode on the kink
profile which couples to the kink translational mode through the damping in the
system. Effective soliton transport is achieved when the internal mode and the
external force get phase locked. We find that for kinks driven by bi-harmonic
drivers consisting of the superposition of a fundamental driver with its first
odd harmonic, the transport arises only due to this {\it internal mode}
mechanism, while for bi-harmonic drivers with even harmonic superposition, also
a point-particle contribution to the drift velocity is present. The phenomenon
is robust enough to survive the presence of thermal noise in the system and can
lead to several interesting physical applications.


title: Lax pair for the Adler (lattice Krichever-Novikov) System

abstract:
  In the paper [V. Adler, IMRN {\bf 1} (1998) 1--4] a lattice version of the
Krichever-Novikov equation was constructed. We present in this note its Lax
pair and discuss its elliptic form.


title:
First degree birational transformations of the Painlev\'e equations and
  their contiguity relations

abstract:
  We present a consistent truncation, allowing us to obtain the first degree
birational transformation found by Okamoto for the sixth Painlev\'e equation.
The discrete equation arising from its contiguity relation is then just the sum
of six simple poles. An algebraic solution is presented, which is equivalent to
but simpler than the Umemura solution. Finally, the well known confluence
provides a unified picture of all first degree birational transformations for
the lower Painlev\'e equations, ranging them in two distinct sequences.


title: Perturbation theory for nearly integrable multi-component nonlinear PDEs

abstract:
  The Riemann-Hilbert problem associated with the integrable PDE is used as a
nonlinear transformation of the nearly integrable PDE to the spectral space.
The temporal evolution of the spectral data is derived with account for
arbitrary perturbations and is given in the form of exact equations, which
generate the sequence of approximate ODEs in successive orders with respect to
the perturbation. For vector nearly integrable PDEs, embracing the vector NLS
and complex modified KdV equations, the main result is formulated in a theorem.
For a single vector soliton the evolution equations for the soliton parameters
and first-order radiation are given in explicit form


title:
Discrete $Z^{\gamma}$: embedded circle patterns with the combinatorics
  of the square grid and discrete Painlev\'e equations

abstract:
  A discrete analog of the holomorphic map $z^{\gamma}$ is studied. It is given
by Schramm's circle pattern with the combinatorics of the square grid. It is
shown that the corresponding circle patterns are embedded and described by
special separatrix solutions of discrete Painlev\'e equations. Global
properties of these solutions, as well as of the discrete $z^{\gamma}$, are
established.


title:
A truncation for obtaining all the first degree birational
  transformations of the Painlev\'e transcendents

abstract:
  A birational transformation is one which leaves invariant an ordinary
differential equation, only changing its parameters. We first recall the
consistent truncation which has allowed us to obtain the first degree
birational transformation of Okamoto for the master Painlev\'e equation P6.
Then we improve it by adding a preliminary step, which is to find all the
Riccati subequations of the considered Pn before performing the truncation. We
discuss in some detail the main novelties of our method, taking as an example
the simplest Painlev\'e equation for that purpose, P2. Finally, we apply the
method to P5 and obtain its two inequivalent first degree birational
transformations.


title:
Scaling properties in dynamics of non-analytic complex maps near the
  accumulation point of the period-tripling cascade

abstract:
  The accumulation point of the period-tripling bifurcation cascade in complex
quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv.
38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett.
A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps,
not necessary satisfying the Cauchy - Riemann equations, the scaling properties
associated with the period-tripling are governed by two relevant universal
complex constants. The first one is $\delta_1 = 4.6002-8.9812i$ (in accordance
with the mentioned works), while the other one, responsible for the violation
of the analyticity, is found to be $\delta_2 = 2.5872+1.8067i$. It means that
in the extended parameter space the critical behaviour associated with the
period-tripling cascade is a phenomenon of codimension four. Scaling properties
of the parameter space are illustrated by diagrams in special local
coordinates. We emphasize a necessity for a nonlinear parameter change to
observe the parameter space scaling.


title: Generation of lattice structures of optical vortices

abstract:
  We demonstrate experimentally the generation of square and hexagonal lattices
of optical vortices and reveal their propagation in a saturable nonlinear
medium. If the topological charges of the vortices are of the same sign the
lattice exhibit rotation, while if alternative, we observe stable propagation
of the structures. In the nonlinear medium the lattices induce periodic
modulation of the refractive index. Diffraction of a probe beam by this
nonlinearity-induced periodic structure is observed.


title: Transient vortex events in the initial value problem for turbulence

abstract:
  A vorticity surge event that could be a paradigm for a wide class of bursting
events in turbulence is studied to examine how the energy cascade is
established and how this event could serve as a new test of LES turbulence
models. This vorticity surge event is tied to the formation of the energy
cascade in a direct numerical simulation by the traditional signatures of a
turbulent energy cascade such as spectra approaching -5/3 and strongly
Beltramized vortex tubes. A coherent mechanism is suggested by the nearly
simultaneous development of a maximum of the peak vorticity
$\|\omega\|_\infty$, growth of the dissipation, the appearance of a helically
aligned local vortex configuration and strong, transient oscillations in the
helicity wavenumber spectrum. This coherence is also examined for two LES
models, a traditional purely dissipative eddy viscosity model and a modern
method (LANS$-\alpha$) that respects the nonlinear transport properties of
fluids. Both LES models properly represent the spectral energy and energy
dissipation associated with this vorticity surge event. However, only the model
that preserves nonlinear fluid transport properties reproduces the helical
properties, including Beltrami-like vortex tubes.


title: Extension of the discrete KP hierarchy

abstract:
  We introduce the discrete hierarchy which naturally generalizes well known
discrete KP hierarchy.


title: Critical Points for Random Boolean Networks

abstract:
  A model of cellular metabolism due to S. Kauffman is analyzed. It consists of
a network of Boolean gates randomly assembled according to a probability
distribution. It is shown that the behavior of the network depends very
critically on certain simple algebraic parameters of the distribution. In some
cases, the analytic results support conclusions based on simulations of random
Boolean networks, but in other cases, they do not.


title: Spectral Properties and Synchronization in Coupled Map Lattices

abstract:
  Spectral properties of Coupled Map Lattices are described. Conditions for the
stability of spatially homogeneous chaotic solutions are derived using linear
stability analysis. Global stability analysis results are also presented. The
analytical results are supplemented with numerical examples. The quadratic map
is used for the site dynamics with different coupling schemes such as global
coupling, nearest neighbor coupling, intermediate range coupling, random
coupling, small world coupling and scale free coupling.


title: Elliptic Gaudin models and elliptic KZ Equations

abstract:
  The Gaudin models based on the face-type elliptic quantum groups and the
$XYZ$ Gaudin models are studied. The Gaudin model Hamiltonians are constructed
and are diagonalized by using the algebraic Bethe ansatz method. The
corresponding face-type Knizhnik-Zamolodchikov equations and their solutions
are given.


title: Estimation of Initial Conditions and Secure Communication

abstract:
  We estimate the initial conditions of a multivariable dynamical system from a
scalar signal, using a modified Newton-Raphson method incorporating the time
evolution. We can estimate initial conditions of periodic and chaotic systems
and the required length of scalar signal is very small. We also find that the
information flow from one variable to the other has logarithmic dependence on
time. An important application of the method is in secure communications. The
communication procedure has several advantages as compared to others using
dynamical systems.


title:
Nonlinear Analysis of the Eckhaus Instability: Modulated Amplitude Waves
  and Phase Chaos with Non-zero Average Phase Gradient

abstract:
  We analyze the Eckhaus instability of plane waves in the one-dimensional
complex Ginzburg-Landau equation (CGLE) and describe the nonlinear effects
arising in the Eckhaus unstable regime. Modulated amplitude waves (MAWs) are
quasi-periodic solutions of the CGLE that emerge near the Eckhaus instability
of plane waves and cease to exist due to saddle-node bifurcations (SN). These
MAWs can be characterized by their average phase gradient $\nu$ and by the
spatial period P of the periodic amplitude modulation. A numerical bifurcation
analysis reveals the existence and stability properties of MAWs with arbitrary
$\nu$ and P. MAWs are found to be stable for large enough $\nu$ and
intermediate values of P. For different parameter values they are unstable to
splitting and attractive interaction between subsequent extrema of the
amplitude. Defects form from perturbed plane waves for parameter values above
the SN of the corresponding MAWs. The break-down of phase chaos with average
phase gradient $\nu$ > 0 (``wound-up phase chaos'') is thus related to these
SNs. A lower bound for the break-down of wound-up phase chaos is given by the
necessary presence of SNs and an upper bound by the absence of the splitting
instability of MAWs.

categories: nlin.CD cond-mat.dis-nn math.DS nlin.PS physics.flu-dyn


title: Rotating Convection in an Anisotropic System

abstract:
  We study the stability of patterns arising in rotating convection in weakly
anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy,
either an endogenous characteristic of the system or induced by external
forcing, can stabilize periodic rolls in the K\"uppers-Lortz chaotic regime.
For the particular case of rotating convection with time-modulated rotation
where recently, in experiment, chiral patterns have been observed in otherwise
K\"uppers-Lortz-unstable regimes, we show how the underlying base-flow breaks
the isotropy, thereby affecting the linear growth-rate of convection rolls in
such a way as to stabilize spirals and targets. Throughout we compare
analytical results to numerical simulations of the Swift-Hohenberg equation.


title: Singularity in classical and quantum Kepler Problem with Weak Anisotropy

abstract:
  Anisotropic Kepler problem is investigated by perturbation method in both
classical and quantum mechanics. In classical mechanics, due to the singularity
of the potential, global diffusion in phase space occurs at an arbitrarily
small perturbation parameter. In quantum mechanics, the singularity induces a
large transition amplitude between quasi degenerate eigen states, which
generically decays as $\hbar$ in the semi-classical limit.


title: Families of line-graphs and their quantization

abstract:
  Any directed graph G with N vertices and J edges has an associated line-graph
L(G) where the J edges form the vertices of L(G). We show that the non-zero
eigenvalues of the adjacency matrices are the same for all graphs of such a
family L^n(G). We give necessary and sufficient conditions for a line-graph to
be quantisable and demonstrate that the spectra of associated quantum
propagators follow the predictions of random matrices under very general
conditions. Line-graphs may therefore serve as models to study the
semiclassical limit (of large matrix size) of a quantum dynamics on graphs with
fixed classical behaviour.


title: Plasticity and learning in a network of coupled phase oscillators

abstract:
  A generalized Kuramoto model of coupled phase oscillators with slowly varying
coupling matrix is studied. The dynamics of the coupling coefficients is driven
by the phase difference of pairs of oscillators in such a way that the coupling
strengthens for synchronized oscillators and weakens for non-synchronized
pairs. The system possesses a family of stable solutions corresponding to
synchronized clusters of different sizes. A particular cluster can be formed by
applying external driving at a given frequency to a group of oscillators. Once
established, the synchronized state is robust against noise and small
variations in natural frequencies. The phase differences between oscillators
within the synchronized cluster can be used for information storage and
retrieval.


title:
Hitchin Systems - Symplectic Hecke Correspondence and Two-dimensional
  Version

abstract:
  The aim of this paper is two-fold. First, we define symplectic maps between
Hitchin systems related to holomorphic bundles of different degrees. We call
these maps the Symplectic Hecke Correspondence (SHC) of the corresponding Higgs
bundles. They are constructed by means of the Hecke correspondence of the
underlying holomorphic bundles. SHC allows to construct B\"{a}cklund
transformations in the Hitchin systems defined over Riemann curves with marked
points. We apply the general scheme to the elliptic Calogero-Moser (CM) system
and construct SHC to an integrable $\SLN$ Euler-Arnold top (the elliptic
$\SLN$-rotator). Next, we propose a generalization of the Hitchin approach to
2d integrable theories related to the Higgs bundles of infinite rank. The main
example is an integrable two-dimensional version of the two-body elliptic CM
system. The previous construction allows to define SHC between the
two-dimensional elliptic CM system and the Landau-Lifshitz equation.


title: Chaos in Black holes Surrounded by Electromagnetic Fields

abstract:
  In this paper we prove the occurence of chaos for charged particles moving
around a Schwarzshild black hole, perturbed by uniform electric and magnetic
fields. The appearance of chaos is studied resorting to the Poincare'-Melnikov
method.


title: Direct Chaotic Communication in Microwave Band

abstract:
  We discuss the concept of Direct Chaotic Communication (DCC). The scheme is
based on the following ideas: (1) the chaotic source generates chaotic
oscillations directly in the specified microwave band; (2) information
component is input by means of formation of the appropriate stream of chaotic
radio pulses; (3) envelope detection is used. The principle of communication
scheme is confirmed experimentally in microwave band. The transmission rates of
3.34, 10.0 and up to 70.0 Mbps are demonstrated. his only looks like the
abstract.


title: Bethe Ansatz solution for quantum spin-1 chains with boundary terms

abstract:
  The procedure for obtaining integrable open spin chain Hamiltonians via
reflection matrices is explicitly carried out for some three-state vertex
models. We have considered the 19-vertex models of Zamolodchikov-Fateev and
Izergin-Korepin, and the $Z_{2}$-graded 19-vertex models with $sl(2|1)$ and
$osp(1|2)$ invariances. In each case the eigenspectrum is determined by
application of the coordinate Bethe Ansatz.


title: Integrability and exact spectrum of a pairing model for nucleons

abstract:
  A pairing model for nucleons, introduced by Richardson in 1966, which
describes proton-neutron pairing as well as proton-proton and neutron-neutron
pairing, is re-examined in the context of the Quantum Inverse Scattering
Method. Specifically, this shows that the model is integrable by enabling the
explicit construction of the conserved operators. We determine the eigenvalues
of these operators in terms of the Bethe ansatz, which in turn leads to an
expression for the energy eigenvalues of the Hamiltonian.


title: Mandelbrot set in coupled logistic maps and in an electronic experiment

abstract:
  We suggest an approach to constructing physical systems with dynamical
characteristics of the complex analytic iterative maps. The idea follows from a
simple notion that the complex quadratic map by a variable change may be
transformed into a set of two identical real one-dimensional quadratic maps
with a particular coupling. Hence, dynamical behavior of similar nature may
occur in coupled dissipative nonlinear systems, which relate to the Feigenbaum
universality class. To substantiate the feasibility of this concept, we
consider an electronic system, which exhibits dynamical phenomena intrinsic to
complex analytic maps. Experimental results are presented, providing the
Mandelbrot set in the parameter plane of this physical system.


title:
Exact anticipating synchronization in bi-directionally coupled
  time-delayed systems

abstract:
  We present an analytical investigation of exact anticipating synchronization
between two bi-idirectionally coupled time-delayed systems in the case when
these systems are governed by two characteristic times: the delay time in the
coupling and the delay time in the coupled systems. We apply our approach to
interpret the results of recent first experimental observation of anticipating
chaos synchronization in external cavity semiconductor lasers with optical
feedback.We establish that our approach can explain the experimental results
only for special cases.


title: Heading towards chaos criterion for quantum field systems

abstract:
  Chaos criterion for quantum field theory is proposed. Its accordance with
classical chaos criterion is demonstrated in the semi-classical limit of
quantum mechanics.


title: Spiral-Logarithmic Structure in a Heisenberg Ferromagnet

abstract:
  Spiral-logarithmic structure is suggested as a stationary solution of a
modified equation for the Heisenberg model, and the single- and N-soliton
solutions are constructed on this base.


title:
Bailout Embeddings, Targeting of KAM Orbits, and the Control of
  Hamiltonian Chaos

abstract:
  We present a novel technique, which we term bailout embedding, that can be
used to target orbits having particular properties out of all orbits in a flow
or map. We explicitly construct a bailout embedding for Hamiltonian systems so
as to target KAM orbits. We show how the bailout dynamics is able to lock onto
extremely small KAM islands in an ergodic sea.


title:
Exact Lag Synchronization in Time Delay Systems and Why Experimental Lag
  Times Can Differ from Theoretical Predictions

abstract:
  We present analytical investigation of exact lag synchronization between two
unidirectionally coupled identical time delay systems with two characteristic
delay times, where the delay time in the coupling is different from the delay
time in the coupled systems themselves. For the first time we demonstrate that
parameter mismatches can explain the experimental observation that the lag time
is equal to the coupling delay.


title: Sequential Bifurcations in Sheared Annular Electroconvection

abstract:
  A sequence of bifurcations is studied in a one-dimensional pattern forming
system subject to the variation of two experimental control parameters: a
dimensionless electrical forcing number ${\cal R}$ and a shear Reynolds number
${\rm Re}$. The pattern is an azimuthally periodic array of traveling vortices
with integer mode number $m$. Varying ${\cal R}$ and ${\rm Re}$ permits the
passage through several codimension-two points. We find that the coefficients
of the nonlinear terms in a generic Landau equation for the primary bifurcation
are discontinuous at the codimension-two points. Further, we map the stability
boundaries in the space of the two parameters by studying the subcritical
secondary bifurcations in which $m \to m+1$ when ${\cal R}$ is increased at
constant ${\rm Re}$.


title:
Noise and Inertia-Induced Inhomogeneity in the Distribution of Small
  Particles in Fluid Flows

abstract:
  The dynamics of small spherical neutrally buoyant particulate impurities
immersed in a two-dimensional fluid flow are known to lead to particle
accumulation in the regions of the flow in which rotation dominates over shear,
provided that the Stokes number of the particles is sufficiently small. If the
flow is viewed as a Hamiltonian dynamical system, it can be seen that the
accumulations occur in the nonchaotic parts of the phase space: the
Kolmogorov--Arnold--Moser tori. This has suggested a generalization of these
dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use
a bailout embedding of the standard map to mimic the dynamics of impurities
subject not only to drag but also to fluctuating forces modelled as white
noise. We find that the generation of inhomogeneities associated with the
separation of particle from fluid trajectories is enhanced by the presence of
noise, so that they appear in much broader ranges of the Stokes number than
those allowing spontaneous separation.


title: Complex Systems As Fundamental Theory Of Sports Coaching?

abstract:
  We argue that traditional Western science cannot adequately describe sports
and other types of human behavior. Then we make an argument why a complex
adaptive systems approach has the potential to provide the foundation for such
a theory. We claim that a special role will be played by biological quantum
computation in the human brain that should have emerged through biological
evolution. Biological quantum computation could have provided evolutionary
advantages in the area of decision-making and fast motor responses, when a
number of potential actions -represented as a set of points in a high
dimensional state-space- are available to the agent. While for animals and
early humans these rapid, coordinated motor activities had direct survival
value, today they are mostly manifested in competitive sports events. We
suggest that entanglement can be facilitated by systematic sports coaching.