title:
Dissipative dynamics of a charged particle in the field of three plane
  waves: chaos and control

abstract:
  The chaotic dissipative dynamics of a charged particle in the field of three
plane waves is theoretically (Melnikov's method) and numerically (Lyapunov
exponents) investigated. In particular, the effectiveness of one of such waves
in controlling the chaotic dynamics induced by the remaining two waves is
theoretically predicted and numerically confirmed. Two mechanisms underlying
the chaos-suppression scenario are identified. One mechanism requires
chaos-inducing and chaos-suppressing waves to have both commensurate
wavelengths and commensurate relative (with respect to the remaining third
wave) phase velocities, while the other mechanism allows the chaotic dynamics
to be tamed when such quantities are incommensurate. The present findings may
be directly applied to several important problems in plasma physics, including
that of the chaos-induced destruction of magnetic surfaces in tokamaks.


title:
Constructing a Supersymmetric Integrable System from the Hirota Method
  in Superspace

abstract:
  An N=1 supersymmetric system is constructed and its integrability is shown by
obtaining three soliton solutions for it using the supersymmetric version of
Hirota's direct method.


title:
Scaling Analysis and Evolution Equation of the North Atlantic
  Oscillation Index Fluctuations

abstract:
  The North Atlantic Oscillation (NAO) monthly index is studied from 1825 till
2002 in order to identify the scaling ranges of its fluctuations upon different
delay times and to find out whether or not it can be regarded as a Markov
process. A Hurst rescaled range analysis and a detrended fluctuation analysis
both indicate the existence of weakly persistent long range time correlations
for the whole scaling range and time span hereby studied. Such correlations are
similar to Brownian fluctuations. The Fokker-Planck equation is derived and
Kramers-Moyal coefficients estimated from the data. They are interpreted in
terms of a drift and a diffusion coefficient as in fluid mechanics. All partial
distribution functions of the NAO monthly index fluctuations have a form close
to a Gaussian, for all time lags, in agreement with the findings of the scaling
analyses. This indicates the lack of predictive power of the present NAO
monthly index. Yet there are some deviations for large (and thus rare) events.
Whence suggestions for other measurements are made if some improved
predictability of the weather/climate in the North Atlantic is of interest. The
subsequent Langevin equation of the NAO signal fluctuations is explicitly
written in terms of the diffusion and drift parameters, and a characteristic
time scale for these is given in appendix.

categories: nlin.CD cond-mat.stat-mech nlin.AO physics.comp-ph


title:
Single- and double-vortex vector solitons in self-focusing nonlinear
  media

abstract:
  We study two-component spatial optical solitons carrying an angular momentum
and propagating in a self-focusing saturable nonlinear medium. When one of the
components is small, such vector solitons can be viewed as a self-trapped
vortex beam that guides either the fundamental or first-order guided mode, and
they are classified as single- and double-vortex vector solitons. For such
composite vortex beams, we demonstrate that a large-amplitude guided mode can
stabilize the ring-like vortex beam which usually decays due to azimuthal
modulational instability. We identify different types of these vector vortex
solitons and demonstrate both vortex bistability and mutual stabilization
effect.


title: Resonant enhancement of the jump rate in a double-well potential

abstract:
  We study the overdamped dynamics of a Brownian particle in the double-well
potential under the influence of an external periodic (AC) force with zero
mean. We obtain a dependence of the jump rate on the frequency of the external
force. The dependence shows a maximum at a certain driving frequency. We
explain the phenomenon as a switching between different time scales of the
system: interwell relaxation time (the mean residence time) and the intrawell
relaxation time. Dependence of the resonant peak on the system parameters,
namely the amplitude of the driving force A and the noise strength
(temperature) D has been explored. We observe that the effect is well
pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of
the order of magnitude with respect to the Kramers rate.


title:
On the Liouville-Arnold integrable flows related with quantum algebras
  and their Poissonian representations

abstract:
  Based on the structure of Casimir elements associated with general Hopf
algebras there are constructed Liouville-Arnold integrable flows related with
naturally induced Poisson structures on arbitrary co-algebra and their
deformations. Some interesting special cases including the oscillatory
Heisenberg-Weil algebra related co-algebra structures and adjoint with them
integrable Hamiltonian systems are considered.


title: Existence and characterization of stable ghost orbits in the Henon map

abstract:
  We report a remarkable type of bifurcation: by varying real parameters,
unstable complex orbits may become stable over wide parameter ranges. Thus,
phase diagrams obtained by analizing solely the stability of real solutions may
be incomplete.


title:
Emergence of Specialization from Global Optimizing Evolution in a
  Multi-Agent System

abstract:
  The evolution of specialization in a multi-agent system is studied both by
computer simulation and Markov process model. Many individual agents search for
and exploit resources to get global optimization in an environment without
complete information. With the selection acting on agent specialization at the
level of system and under the condition of increasing returns, the division of
labor emerges as the results of long-term optimizing evolution. Mathematical
analysis gives the optimum division of agents and a Markov chain model is
proposed to describe the evolutionary dynamics. The results are in good
agreement with that of simulation model.


title:
Algebraic Bethe Ansatz solutions for the $sl(2|1)^{(2)}$ and $osp(2|1)$
  models with boundary terms

abstract:
  This work is concerned with the formulation of the graded quantum inverse
scattering method for a class oflattice models with reflecting boundary
conditions. The $sl(2|1)^{(2)}$ and $osp(2|1)$ models are considered with their
diagonal reflections in BFB grading. This allowed us to derive the eigenvalues
and eigenvectors for the corresponding transfer matrices as well as explicit
expressions for the Bethe Ansatz equations.


abstract:
  Fundamental solution of Fokker - Planck equation is built by means of the
Fourier transform method. The result is checked by direct calculation. Changes:
missed factor in (29), (30), corrected (31), (35), removed former (36), added
explanation on prolonged operators (45), (46), (47).


title:
Inherent global stabilization of unstable local behavior in coupled map
  lattices

abstract:
  The behavior of two-dimensional coupled map lattices is studied with respect
to the global stabilization of unstable local fixed points without external
control. It is numerically shown under which circumstances such inherent global
stabilization can be achieved for both synchronous and asynchronous updating.
Two necessary conditions for inherent global stabilization are derived
analytically.


title:
Effect of the Introduction of Impurities on the Stability Properties of
  Multibreathers at Low Coupling

abstract:
  sing a theorem dubbed the {\em Multibreather Stabiliy Theorem} [Physica D 180
(2003) 235-255] we have obtained the stability properties of multibreathers in
systems of coupled oscillators with on-site potentials, with an inhomogeneity.
Analytical results are obtained for 2-site, 3-site breathers, multibreathers,
phonobreathers and dark breathers. The inhomogeneity is considered both at the
on-site potential and at the coupling terms. All the results have been checked
numerically with excellent agreement. The main conclusion is that the
introduction of a impurity does not alter the stability properties.


title: The random growth of interfaces as a subordinated process

abstract:
  We study the random growth of surfaces from within the perspective of a
single column, namely, the fluctuation of the column height around the mean
value, y(t)= h(t)-< h(t)>, which is depicted as being subordinated to a
standard fluctuation-dissipation process with friction gamma. We argue that the
main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by
identifying the distribution of return times to y(0) = 0, which is a truncated
inverse power law, with the distribution of subordination times. The agreement
of the theoretical prediction with the numerical treatment of the 1 + 1
dimensional model of ballistic deposition is remarkably good, in spite of the
finite size effects affecting this model.


title: Stabilization of causally and non-causally coupled map lattices

abstract:
  Two-dimensional coupled map lattices have global stability properties that
depend on the coupling between individual maps and their neighborhood. The
action of the neighborhood on individual maps can be implemented in terms of
"causal" coupling (to spatially distant past states) or "non-causal" coupling
(to spatially distant simultaneous states). In this contribution we show that
globally stable behavior of coupled map lattices is facilitated by causal
coupling, thus indicating a surprising relationship between stability and
causality. The influence of causal versus non-causal coupling for synchronous
and asynchronous updating as a function of coupling strength and for different
neighborhoods is analyzed in detail.


title: The morphology of nodal lines-random waves versus percolation

abstract:
  In this paper we investigate the properties of nodal structures in random
wave fields, and in particular we scrutinize their recently proposed connection
with short-range percolation models. We propose a measure which shows the
difference between monochromatic random waves, which are characterized by
long-range correlations, and Gaussian fields with short-range correlations,
which are naturally assumed to be better modelled by percolation theory. We
also study the relevance of the quantities which we compute to the probability
that nodal lines are in the vicinity of a given reference line.


title: Clustering and collisions of heavy particles in random smooth flows

abstract:
  Finite-size impurities suspended in incompressible flows distribute
inhomogeneously, leading to a drastic enhancement of collisions. A description
of the dynamics in the full position-velocity phase space is essential to
understand the underlying mechanisms, especially for polydisperse suspensions.
These issues are here studied for particles much heavier than the fluid by
means of a Lagrangian approach. It is shown that inertia enhances collision
rates through two effects: correlation among particle positions induced by the
carrier flow and uncorrelation between velocities due to their finite size. A
phenomenological model yields an estimate of collision rates for particle pairs
with different sizes. This approach is supported by numerical simulations in
random flows.


title:
Stability analysis of coupled map lattices at locally unstable fixed
  points

abstract:
  Numerical simulations of coupled map lattices (CMLs) and other complex model
systems show an enormous phenomenological variety that is difficult to classify
and understand. It is therefore desirable to establish analytical tools for
exploring fundamental features of CMLs, such as their stability properties.
Since CMLs can be considered as graphs, we apply methods of spectral graph
theory to analyze their stability at locally unstable fixed points for
different updating rules, different coupling scenarios, and different types of
neighborhoods. Numerical studies are found to be in excellent agreement with
our theoretical results.


title: Slowing and stopping of chemical waves in a narrowing canal

abstract:
  The propagation of a chemical wave in a narrow, cone-shaped glass capillary
was investigated. When a chemical wave propagates from the wider end to the
narrower end, it slows, stops, and then disappears. A phenomenological model
that considers the surface effect of the glass is proposed, and this model
reproduces the experimental trends.


title: On the Treves Criterion for the Boussinesq and other GD Hierarchies

abstract:
  This is an addition to our paper (Lett.Math.Phys 65,2003,187-197) where an
analogue of the Treves criterion for the first integrals of the KdV hierarchy
was suggested for the Boussinesq hierarchy and its necessity was proven. In the
present paper, it is proven that there exists the second, ``conjugated'', group
of tests. Besides, the relationship between our method and the B\"acklund
transformation method recently suggested by Morosi and Pizzocchero is
discussed.


title: Oscillating kinks in forced oscillatory media: A new type of instability

abstract:
  A new type of instability resulting in oscillatory propagating kinks is
presented. It is observed in periodically forced oscillatory media at 1:1
resonance, where phase kinks have close similarities to pulses in excitable
media. Considering the periodically forced complex Ginzburg-Landau equation,
examples for transitions involving oscillating kinks between different
dynamical regimes are described. The oscillatory instability is discussed
within the framework of a bifurcation analysis of the kink profiles


title: Active and passive fields face to face

abstract:
  The statistical properties of active and passive scalar fields transported by
the same turbulent flow are investigated. Four examples of active scalar have
been considered: temperature in thermal convection, magnetic potential in
two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman
turbulence and potential temperature in surface flows. In the cases of
temperature and vorticity, it is found that the active scalar behavior is akin
to that of its co-evolving passive counterpart. The two other cases indicate
that this similarity is in fact not generic and differences between passive and
active fields can be striking: in two-dimensional magnetohydrodynamics the
magnetic potential performs an inverse cascade while the passive scalar
cascades toward the small-scales; in surface flows, albeit both perform a
direct cascade, the potential temperature and the passive scalar have different
scaling laws already at the level of low-order statistical objects. These
dramatic differences are rooted in the correlations between the active scalar
input and the particle trajectories. The role of such correlations in the issue
of universality in active scalar transport and the behavior of dissipative
anomalies is addressed.


title:
Self-organized pulses of dynamic systems with three-dimensional phase
  space

abstract:
  The possibility of production of pulses with scale-invariant properties at
presence of fluctuations of parameters of self-oscillatory system with
three-dimensional phase space is shown. The system of equations of inertial
nonlinearity oscillator is numerically investigated. The formulas of
quantitative characteristics of the form and self-similar values of
informational entropy of complex pulses allowing to extract self-organized
signals are obtained.


title: Extended discrete KP hierarchy and its dispersionless limit

abstract: We exhibit the dispersionless limit of the extended discrete KP hierarchy.


title: Localization in the non-analytic quantum kicked systems

abstract:
  Numerical investigations on non-analytic quantum kicked systems are
presented. A new type of localization - power-law localization is found to be
universal in the nonanalytic systems. With increasing the perturbation
strength, a transition from perturbative localization to pseudo-integrable
system, to dynamical localization and to complete extension is clearly
demonstrated. The dependence of the localization length on perturbation is
given in different parameter regimes.


title:
Solutions of Certain Types of Linear and Nonlinear Diffusion-Reaction
  Equations in One Dimension

abstract:
  With a view to having further insight into the mathematical content of the
non-Hermitian Hamiltonian associaterd with the diffusion-reaction (D-R)
equation in one dimension, we investigate (a) the solitary wave solutions of
certain types of its nonlinear versions, and (b) the problem of real eigenvalue
spectrum associated with its linear version or with this class of non-Hermitian
Hamiltonians. For the case (a) we use the standard techniques to handle the
quadratic and cubic nonlinearities in the D-R equation whereas for the case (b)
a newly proposed method, based on an extended complex phase space, is employed.
For a particular class of solutions, an Ermakov system of equations is also
found for the linear case. Further, corresponding to the 'classical' version of
the above one-dimensional complex Hamiltonian, an equivalent integrable system
of two, two-dimensional real Hamiltonians is suggested.


title: Oscillating tails of dispersion-managed soliton

abstract:
  Oscillating tails of dispersion-managed optical fiber system are studied for
strong dispersion map in the framework of path-averaged Gabitov-Turitsyn
equation. The small parameter of the analytical theory is the inverse time. An
exponential decay in time of soliton tails envelope is consistent with nonlocal
nonlinearity of Gabitov-Turitsyn equation, and the fast oscillations are
described by a quadratic law. The pre-exponential modification factor is the
linear function of time for zero average dispersion and cubic function for
nonzero average dispersion.


title: Synchronization of networks with prescribed degree distributions

abstract:
  We show that the degree distributions of graphs do not suffice to
characterize the synchronization of systems evolving on them. We prove that,
for any given degree sequence satisfying certain conditions, there exists a
connected graph having that degree sequence for which the first nontrivial
eigenvalue of the graph Laplacian is arbitrarily close to zero. Consequently,
complex dynamical systems defined on such graphs have poor synchronization
properties. The result holds under quite mild assumptions, and shows that there
exists classes of random, scale-free, regular, small-world, and other common
network architectures which impede synchronization. The proof is based on a
construction that also serves as an algorithm for building non-synchronizing
networks having a prescribed degree distribution.


title: On the Treves theorem for the AKNS equation

abstract:
  According to a theorem of Treves, the conserved functionals of the AKNS
equation vanish on all pairs of formal Laurent series of a specified form, both
of them with a pole of the first order. We propose a new and very simple proof
for this statement, based on the theory of B\"acklund transformations; using
the same method, we prove that the AKNS conserved functionals vanish on other
pairs of Laurent series. The spirit is the same of our previous paper on the
Treves theorem for the KdV, with some non trivial technical differences.


title: Solitary waves of nonlinear nonintegrable equations

abstract:
  Our goal is to find closed form analytic expressions for the solitary waves
of nonlinear nonintegrable partial differential equations. The suitable
methods, which can only be nonperturbative, are classified in two classes.
  In the first class, which includes the well known so-called truncation
methods, one \textit{a priori} assumes a given class of expressions
(polynomials, etc) for the unknown solution; the involved work can easily be
done by hand but all solutions outside the given class are surely missed.
  In the second class, instead of searching an expression for the solution, one
builds an intermediate, equivalent information, namely the \textit{first order}
autonomous ODE satisfied by the solitary wave; in principle, no solution can be
missed, but the involved work requires computer algebra.
  We present the application to the cubic and quintic complex one-dimensional
Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation.


title: Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries

abstract:
  We diagonalize the double-row transfer matrix of the SU(N) vertex model for
certain classes of non-diagonal boundary conditions. We derive explicit
expressions for the corresponding eigenvectors and eigenvalues by means of the
algebraic Bethe ansatz approach.


title:
Photoabsorption spectra of the diamagnetic hydrogen atom in the
  transition regime to chaos: Closed orbit theory with bifurcating orbits

abstract:
  With increasing energy the diamagnetic hydrogen atom undergoes a transition
from regular to chaotic classical dynamics, and the closed orbits pass through
various cascades of bifurcations. Closed orbit theory allows for the
semiclassical calculation of photoabsorption spectra of the diamagnetic
hydrogen atom. However, at the bifurcations the closed orbit contributions
diverge. The singularities can be removed with the help of uniform
semiclassical approximations which are constructed over a wide energy range for
different types of codimension one and two catastrophes. Using the uniform
approximations and applying the high-resolution harmonic inversion method we
calculate fully resolved semiclassical photoabsorption spectra, i.e.,
individual eigenenergies and transition matrix elements at laboratory magnetic
field strengths, and compare them with the results of exact quantum
calculations.


title:
Brownian motion and diffusion: from stochastic processes to chaos and
  beyond

abstract:
  One century after Einstein's work, Brownian Motion still remains both a
fundamental open issue and a continous source of inspiration for many areas of
natural sciences. We first present a discussion about stochastic and
deterministic approaches proposed in the literature to model the Brownian
Motion and more general diffusive behaviours. Then, we focus on the problems
concerning the determination of the microscopic nature of diffusion by means of
data analysis. Finally, we discuss the general conditions required for the
onset of large scale diffusive motion.


title: Trihamiltonian extensions of separable systems in the plane

abstract:
  A method to construct trihamiltonian extensions of a separable system is
presented. The procedure is tested for systems, with a natural Hamiltonian,
separable in classical sense in one of the four orthogonal separable coordinate
systems of the Euclidean plane, and some explicit examples are constructed.
Finally a conjecture on possible generalizations to other classes of systems is
discussed: in particular, the method can be easily adapted to the eleven
orthogonal separable coordinate sets of the Euclidean three-space.


title: Wind reversals in turbulent Rayleigh-Benard convection

abstract:
  The phenomenon of irregular cessation and subsequent reversal of the
large-scale circulation in turbulent Rayleigh-B\'enard convection is
theoretically analysed. The force and thermal balance on a single plume
detached from the thermal boundary layer yields a set of coupled nonlinear
equations, whose dynamics is related to the Lorenz equations. For Prandtl and
Rayleigh numbers in the range $10^{-2} \leq \Pr \leq 10^{3}$ and $10^{7} \leq
\Ra \leq 10^{12}$, the model has the following features: (i) chaotic reversals
may be exhibited at Ra $\geq 10^{7}$; (ii) the Reynolds number based on the
root mean square velocity scales as $\Re_{rms} \sim \Ra^{[0.41 ...
  0.47]}$ (depending on Pr), and as $\Re_{rms} \sim \Pr^{-[0.66 ... 0.76]}$
(depending on Ra); and (iii) the mean reversal frequency follows an effective
scaling law $\omega / (\nu L^{-2}) \sim \Pr^{-(0.64 \pm 0.01)} \Ra^{0.44 \pm
0.01}$. The phase diagram of the model is sketched, and the observed
transitions are discussed.


title:
Application of Artificial Neural Network in Jitter Analysis of
  Dispersion-Managed Communication System

abstract:
  Artificial Neural Network (ANN) is used as numerical methode in solving
modified Nonlinear Schroedinger (NLS) equation with Dispersion Managed System
(DMS) for jitter analysis. We take the optical axis z and the time t as input,
and then some relevant values such as the change of position and the center
frequency of the pulse, and further the mean square time of incoming pulse
which are needed for jitter analysis. It shows that ANN yields numerical
solutions which are adaptive with respect to the numerical errors and also
verifies the previous numerical results using conventional numerical method.
Our result indicates that DMS can minimize the timing jitter induced by some
amplifiers.


title:
Base of nonlinear dynamics or Real Dynamics, Ideal Dynamics,
  Unpredictable Dynamics and "Schrodinger cat"

abstract:
  In the paper paradoxes underlying thermodynamics and a quantum mechanics are
discussed. Their solution is given from the point of view of influence of the
exterior observer (surrounding medium) destroying correlations of system, or
boundedness of self-knowledge of system in a case when both the observer, and a
surrounding medium are included in system. Concepts Real Dynamics, Ideal
Dynamics and Unpredictable Dynamics are entered. Consideration an appearance of
a life is given from the point of view of these three Dynamics.


title: Square vortex solitons with a large angular momentum

abstract:
  We show the existence of square shaped optical vortices with a large value of
the angular momentum hosted in finite size laser beams which propagate in
nonlinear media with a cubic-quintic nonlinearity. The light profiles take the
form of rings with sharp boundaries and variable sizes depending on the power
carried. Our stability analysis shows that these light distributions remain
stable when propagate, probably for unlimited values of the angular momentum,
provided the hosting beam is wide enough. This happens if the peak amplitude
approaches a critical value which only depends on the nonlinear refractive
index of the material. A variational approach allows us to calculate the main
parameters involved. Our results add extra support to the concept of surface
tension of light beams that can be considered as a trace of the existence of a
liquid of light.


title: On a class of three-dimensional integrable Lagrangians

abstract:
  We characterize non-degenerate Lagrangians of the form $ \int f(u_x, u_y,
u_t) dx dy dt $ such that the corresponding Euler-Lagrange equations $
(f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of
hydrodynamic reductions. The integrability conditions constitute an
over-determined system of fourth order PDEs for the Lagrangian density $f$,
which is in involution and possess interesting differential-geometric
properties. The moduli space of integrable Lagrangians, factorized by the
action of a natural equivalence group, is three-dimensional. Familiar examples
include the dispersionless Kadomtsev-Petviashvili (dKP) and the Boyer-Finley
Lagrangians, $f=u_x^3/3+u_y^2-u_xu_t$ and $f=u_x^2+u_y^2-2e^{u_t}$,
respectively. A complete description of integrable cubic and quartic
Lagrangians is obtained. Up to the equivalence transformations, the list of
integrable cubic Lagrangians reduces to three examples, $ f=u_xu_yu_t,
f=u_x^2u_y+u_yu_t, and f=u_x^3/3+u_y^2-u_xu_t ({\rm dKP}).$ There exists a
unique integrable quartic Lagrangian, $ f=u_x^4+2u_x^2u_t-u_xu_y-u_t^2.$ We
conjecture that these examples exhaust the list of integrable polynomial
Lagrangians which are essentially three-dimensional (it was verified that there
exist no polynomial integrable Lagrangians of degree five). We prove that the
Euler-Lagrange equations are integrable by the method of hydrodynamic
reductions if and only if they possess a scalar pseudopotential playing the
role of a dispersionless `Lax pair'. MSC: 35Q58, 37K05, 37K10, 37K25. Keywords:
Multi-dimensional Dispersionless Integrable Systems, Hydrodynamic Reductions,
Pseudopotentials.


title: Bistability between different dissipative solitons in nonlinear optics

abstract:
  We report the observation of different localized structures coexisting for
the same parameter values in an extended system. The experimental findings are
carried out in a nonlinear optical interferometer, and are fully confirmed by
numerical simulations. The existence of each kind of localized structure is put
in relation to a corresponding delocalized pattern observed. Quantitative
evaluation of the range of pump parameter allowing bistability between
localized structures is given. The dependence of the phenomena on the other
relevant parameters is discussed.


title:
Stable propagation of pulsed beams in Kerr focusing media with modulated
  dispersion

abstract:
  We propose the modulation of dispersion to prevent collapse of planar pulsed
beams which propagate in Kerr-type self-focusing optical media. As a result, we
find a new type of two-dimensional spatio-temporal solitons stabilized by
dispersion management. We have studied the existence and properties of these
solitary waves both analytically and numerically. We show that the adequate
choice of the modulation parameters optimizes the stabilization of the pulse.


title: A study on a self-organized criticality in a dynamical many-body system

abstract:
  A novel mechanism for the generation of self-organized criticality (SOC) is
discussed in terms of the coupled-vibration model where the total system is
forced under the uniform expansion of the Hubble type. This system shows a
robust SOC behavior while the maximum size of the fluctuation, number of
correlated particles in it and the temporal size of the system evolve as a
function of time.


title: Direct transition to high-dimensional chaos through a global bifurcation

abstract:
  In the present work we report on a genuine route by which a high-dimensional
(with d>4) chaotic attractor is created directly, i.e., without a
low-dimensional chaotic attractor as an intermediate step. The high-dimensional
chaotic set is created in a heteroclinic global bifurcation that yields an
infinite number of unstable tori.The mechanism is illustrated using a system
constructed by coupling three Lorenz oscillators. So, the route presented here
can be considered a prototype for high-dimensional chaotic behavior just as the
Lorenz model is for low-dimensional chaos.


title:
Adaptive Boolean Networks and Minority Games with Time--Dependent
  Capacities

abstract:
  In this paper we consider a network of boolean agents that compete for a
limited resource. The agents play the so called Generalized Minority Game where
the capacity level is allowed to vary externally. We study the properties of
such a system for different values of the mean connectivity $K$ of the network,
and show that the system with K=2 shows a high degree of coordination for
relatively large variations of the capacity level.


title:
$A_{2}^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov
  equation

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


title: Chaotic Root-Finding for a Small Class of Polynomials

abstract:
  In this paper we present a new closed-form solution to a chaotic difference
equation, y(n+1) = a2 y(n)^2 + a1 y(n) + a0 with coefficient a0 = (a1 - 4)(a1 +
2) / (4 a2) and using this solution, show how corresponding exact roots to a
special set of related polynomials of order 2^p, p in the naturals, with two
independent parameters can be generated, for any p.


title: Spatial coherence singularities of a vortex field in nonlinear media

abstract:
  We study the spatial coherence properties of optical vortices generated by
partially incoherent light in self-focusing nonlinear media. We reveal the
existence of phase singularities in the spatial coherence function of a vortex
field that can characterize the stable propagation of vortices through
nonlinear media.


title: From collective rhythm to adaptive synchronization

abstract:
  A novel viewpoint, i.e., adaptive synchronization, is proposed to explore
collective rhythm observed in many complex, self-organizing systems. We show
that a simple adaptive coupling is able to tip arrays of oscillators towards
collective synchronization. Two arrays of simply coupled Hindmarsh-Rose chaotic
neurons are used to illustrate cooperative dynamics of neural activity like the
central pattern generators, which supplies a new idea for biological
experiments and numerical simulations. The results enhance the viewpoint that
chaos is a necessary ingredient in life, and indicate that such small-world
adaptive coupling may be a universal essence of the collective rhythm observed
in nature.


title: Chimera States for Coupled Oscillators

abstract:
  Arrays of identical oscillators can display a remarkable spatiotemporal
pattern in which phase-locked oscillators coexist with drifting ones.
Discovered two years ago, such "chimera states" are believed to be impossible
for locally or globally coupled systems; they are peculiar to the intermediate
case of nonlocal coupling. Here we present an exact solution for this state,
for a ring of phase oscillators coupled by a cosine kernel. We show that the
stable chimera state bifurcates from a spatially modulated drift state, and
dies in a saddle-node bifurcation with an unstable chimera.


title: Complementarity in classical dynamical systems

abstract:
  The concept of complementarity, originally defined for non-commuting
observables of quantum systems with states of non-vanishing dispersion, is
extended to classical dynamical systems with a partitioned phase space.
Interpreting partitions in terms of ensembles of epistemic states (symbols)
with corresponding classical observables, it is shown that such observables are
complementary to each other with respect to particular partitions unless those
partitions are generating. This explains why symbolic descriptions based on an
\emph{ad hoc} partition of an underlying phase space description should
generally be expected to be incompatible. Related approaches with different
background and different objectives are discussed.


title:
A phenomenological model of weakly damped Faraday waves and the
  associated mean flow

abstract:
  A phenomenological model of parametric surface waves (Faraday waves) is
introduced in the limit of small viscous dissipation that accounts for the
coupling between surface motion and slowly varying streaming and large scale
flows (mean flow). The primary bifurcation of the model is to a set of standing
waves (stripes, given the functional form of the model nonlinearities chosen
here). Our results for the secondary instabilities of the primary wave show
that the mean flow leads to a weak destabilization of the base state against
Eckhaus and Transverse Amplitude Modulation instabilities, and introduces a new
longitudinal oscillatory instability which is absent without the coupling. We
compare our results with recent one dimensional amplitude equations for this
system systematically derived from the governing hydrodynamic equations.


title: Channelling chaos by building barriers

abstract:
  Chaos often represents a severe obstacle for the set-up of many-body
experiments, e.g., in fusion plasmas or turbulent flows. We propose a strategy
to control chaotic diffusion in conservative systems. The core of our approach
is a small apt modification of the system which channels chaos by building
barriers to diffusion. It leads to practical prescriptions for an experimental
apparatus to operate in a regular regime (drastic enhancement of confinement).
The experimental realization of this control on a Travelling Wave Tube opens
the possibility to practically achieve the control of a wide range of systems
at a low additional cost of energy.


title:
Oscillatory phase transition and pulse propagation in noisy
  integrate-and-fire neurons

abstract:
  We study non-locally coupled noisy integrate-and-fire neurons with the
Fokker-Planck equation. A propagating pulse state and a wavy state appear as a
phase transition from an asynchronous state. We also find a solution in which
traveling pulses are emitted periodically from a pacemaker region.


title: Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach

abstract:
  A proper bilinear form is proposed for the N=1 supersymmetric modified
Korteweg-de Vries equation. The bilinear B\"{a}cklund transformation of this
system is constructed. As applications, some solutions are presented for it.


title:
The Domain Chaos Puzzle and the Moments of the Swift-Hohenberg Structure
  Factor

abstract:
  This paper is being extensively rewritten and will be resubmitted in a
different form.


title: Breaking a chaos-noise-based secure communication scheme

abstract:
  This paper studies the security of a secure communication scheme based on two
discrete-time intermittently-chaotic systems synchronized via a common random
driving signal. Some security defects of the scheme are revealed: 1) the key
space can be remarkably reduced; 2) the decryption is insensitive to the
mismatch of the secret key; 3) the key-generation process is insecure against
known/chosen-plaintext attacks. The first two defects mean that the scheme is
not secure enough against brute-force attacks, and the third one means that an
attacker can easily break the cryptosystem by approximately estimating the
secret key once he has a chance to access a fragment of the generated
keystream. Yet it remains to be clarified if intermittent chaos could be used
for designing secure chaotic cryptosystems.


title: Complexity vs stability in small-world networks

abstract:
  According to the May-Wigner stability theorem, increasing the complexity of a
network inevitably leads to its destabilization, such that a small perturbation
will be able to disrupt the entire system. One of the principal arguments
against this observation is that it is valid only for random networks, and
therefore does not apply to real-world networks, which presumably are
structured. Here we examine how the introduction of small-world topological
structure into networks affect their stability. Our results indicate that, in
structured networks, the parameter values at which the stability-instability
transition occurs with increasing complexity is identical to that predicted by
the May-Wigner criteria. However, the nature of the transition, as measured by
the finite-size scaling exponent, appears to change as the network topology
transforms from regular to random, with the small-world regime as the
cross-over region. This behavior is related to the localization of the largest
eigenvalues along the real axis in the eigenvalue plain with increasing
regularity in the network.


title:
Coarse-grained periodic orbits and bifurcations in a Markov chain model
  for evolution of labor division

abstract:
  We construct a Markov process model to describe the evolution of labor
division and its dynamical behavior is investigated by numerical simulations in
detail. We have shown that under the mechanism of increasing returns, the
division of labor will emerge from the initial homogenous distribution and with
the change of parameters there are period-adding coarse-grained bifurcations in
the model. The model gives an example of emergent property in the evolution of
complex systems and reveals an interesting dynamical behavior of the Markov
chain process. Key words: Evolution, Bifurcation, Pattern formation PACS
number(s): 87.23.-n, 89.75.Fb, 05.45.-a


title:
Multifractal nature of plume structure in high Rayleigh number
  convection

abstract:
  The geometrically different plan forms of near wall plume structure in
turbulent natural convection, visualised by driving the convection using
concentration differences across a membrane, are shown to have a common
multifractal spectrum of singularities for Rayleigh numbers in the range
$10^{10}- 10^{11}$ at Schmidt number of 602. The scaling is seen for a length
scale range of $2^5$ and is independent of the Rayleigh number, the flux, the
strength and nature of the large scale flow, and the aspect ratio. Similar
scaling is observed for the plume structures obtained in the presence of a weak
flow across the membrane. This common non trivial spatial scaling is proposed
to be due to the same underlying generating process of the near wall plume
structures.


title:
The production rate of the coarse grained Gibbs entropy and the
  Kolmogorov-Sinai entropy: a real connection ?

abstract:
  We discuss the connection between the Kolmogorov-Sinai entropy, $h_{KS}$, and
the production rate of the coarse grained Gibbs entropy, $r_G$. Detailed
numerical computations show that the (often accepted) identification of the two
quantities does not hold in systems with intermittent behavior and/or very
different characteristic times and in systems presenting pseudo-chaos. The
basic reason of this fact is in the asymptotic (with respect to time) nature of
$h_{KS}$, while $r_G$ is a quantity related to short time features of a system.


title:
On the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym
  equations

abstract:
  We show that the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym
hierarchies can be obtained by applying a reduction process to a simple Poisson
pair defined on the loop algebra of $\mathfrak{sl}(2,\mathbb{R})$. The
reduction process is a bi-Hamiltonian reduction, that can be canonically
performed on every bi-Hamiltonian manifold.


title:
Breaking projective chaos synchronization secure communication using
  filtering and generalized synchronization

abstract:
  This paper describes the security weaknesses of a recently proposed secure
communication method based on chaotic masking using projective synchronization
of two chaotic systems. We show that the system is insecure and how to break it
in two different ways, by high-pass filtering and by generalized
synchronization.


title:
First numerical evidence of global Arnold diffusion in quasi--integrable
  systems

abstract:
  We provide numerical evidence of global diffusion occurring in slightly
perturbed integrable Hamiltonian systems and symplectic maps. We show that even
if a system is sufficiently close to be integrable, global diffusion occurs on
a set with peculiar topology, the so--called Arnold web, and is qualitatively
different from Chirikov diffusion, occurring in more perturbed systems.


title: A Hamiltonian system for interacting Benjamin-Feir resonances

abstract:
  In this paper, we present a model describing the time evolution of two
dimensional surface waves in gravity and infinite depth. The model of six
interacting modes derives from the normal form of the system describing the
dynamics of surface waves and is governed by a Hamiltonian system of equations
of cubic order in the amplitudes of the waves. We derive a Hamiltonian system
with two degrees of freedom from this Hamiltonian using conserved quantities.
The interactions are those of two coupled Benjamin-Feir resonances. The
temporal evolution of the amplitude of the different modes is described
according to the parameters of the system. In particular, we study the energy
exchange produced by the modulations of the amplitudes of the modes. The
evolution of the modes reveals a chaotic dynamics.


title:
Classical dynamics near the triple collision in a three-body Coulomb
  problem

abstract:
  We investigate the classical motion of three charged particles with both
attractive and repulsive interaction.The triple collision is a main source of
chaos in such three body Coulomb problems.By employing the McGehee scaling
technique, we analyse here for the first time in detail the three-body dynamics
near the triple collision in 3 degrees of freedom.We reveal surprisingly simple
dynamical patterns in large parts of the chaotic phase space. The underlying
degree of order in the form of approximate Markov partitions may help in
understanding the global structures observed in quantum spectra of two-electron
atoms.


title:
Construction of Single-valued Solutions for Nonintegrable Systems with
  the Help of the Painleve Test

abstract:
  The Painleve test is very useful to construct not only the Laurent-series
solutions but also the elliptic and trigonometric ones. Such single-valued
functions are solutions of some polynomial first order differential equations.
To find the elliptic solutions we transform an initial nonlinear differential
equation in a nonlinear algebraic system in parameters of the Laurent-series
solutions of the initial equation. The number of unknowns in the obtained
nonlinear system does not depend on number of arbitrary coefficients of the
used first order equation. In this paper we describe the corresponding
algorithm, which has been realized in REDUCE and Maple.

categories: nlin.SI astro-ph.SR cs.MS math-ph math.DS math.MP


title: Symmetry algebras for superintegrable systems

abstract:
  It is shown that the symmetry algebra of quantum superintegrable system can
be always chosen to be u(N),N being the number of degrees of freedom.


title:
Quadratic integrals of motions for the systems of identical
  particles-quantum case

abstract:
  The quantum dynamical systems of identical particles admitting an additional
integral quadratic in momenta are considered. It is found that an appropriate
ordering procedure exists which allows to convert the classical integrals into
their quantum counterparts. The relation to the separation of variables in
Schroedinger equation is discussed.


title: Quadratic integrals of motion for the systems of identical particles

abstract:
  The dynamical systems of identical particles admitting quadratic integrals of
motion are classified. The relevant integrals are explicitly constructed and
their relation to separation of variables in H-J equation is clarified.


title:
Dirty, Skewed, and Backwards: The Smectic $A$-$C$ Phase Transition in
  Aerogel

abstract:
  We study the smectic AC transition in anisotropic and uniaxial disordered
environments, e.g., aerogel with an external field. We find very strange
behavior of translational correlations: the low-temperature, lower-symmetry
Smectic C phase is itless translationally ordered than the it high-temperature,
higher-symmetry Smectic A phase, with short-ranged and algebraic translational
correlations, respectively. Specifically, the A and C phase belong to the
quasi-long-ranged translationally ordered " XY Bragg glass '' and short-ranged
translationally ordered " m=1 Bragg glass '' phase, respectively. The AC phase
transition itself belongs to a new universality class, whose fixed points and
exponents we find in a d=5-epsilon expansion.


title:
An improved $\eps$ expansion for three-dimensional turbulence: two-loop
  renormalization near two dimensions

abstract:
  An improved $\eps$ expansion in the $d$-dimensional ($d > 2$) stochastic
theory of turbulence is constructed at two-loop order which incorporates the
effect of pole singularities at $d \to 2$ in coefficients of the $\eps$
expansion of universal quantities. For a proper account of the effect of these
singularities two different approaches to the renormalization of the powerlike
correlation function of the random force are analyzed near two dimensions. By
direct calculation it is shown that the approach based on the mere
renormalization of the nonlocal correlation function leads to contradictions at
two-loop order. On the other hand, a two-loop calculation in the
renormalization scheme with the addition to the force correlation function of a
local term to be renormalized instead of the nonlocal one yields consistent
results in accordance with the UV renormalization theory. The latter
renormalization prescription is used for the two-loop renormalization-group
analysis amended with partial resummation of the pole singularities near two
dimensions leading to a significant improvement of the agreement with
experimental results for the Kolmogorov constant.


title:
Acceleration Statistics as Measures of Statistical Persistence of
  Streamlines in Isotropic Turbulence

abstract:
  We introduce the velocity (Vs) of stagnation points as a means to
characterise and measure statistical persistence of streamlines. Using
theoretical arguments, Direct Numerical Simulations (DNS) and Kinematic
Simulations (KS) of three-dimensional isotropic turbulence for different ratios
of inner to outer length scales L/eta of the self-similar range, we show that a
frame exists where the average <Vs>=0, that the r.m.s. values of acceleration
(a'), turbulent fluid velocity (u') and Vs are related by La'/(u'^2) ~
(Vs/u')(L/eta)^(2/3+q) and that Vs/u' ~ (L/eta)^q with q=-1/3 in Kolmogorov
turbulence, q=-1/6 in current DNS and q=0 in our KS. The statistical
persistence hypothesis is closely related to the Tennekes sweeping hypothesis.


title: Integrability of a Non-autonomous Coupled KdV System

abstract:
  The Painlev\'{e} property of coupled, non-autonomous Korteweg-de Vries (KdV)
type of systems is studied. The conditions under which the systems pass the
Painlev\'{e} test for integrability are obtained. For some of the integrable
cases, exact solutions are given.


title: Factorization methods for Noncommutative KP and Toda hierarchy

abstract:
  We show that the solution space of the noncommutative KP hierarchy is the
same as that of the commutative KP hierarchy owing to the Birkhoff
decomposition of groups over the noncommutative algebra. The noncommutative
Toda hierarchy is introduced. We derive the bilinear identities for the
Baker--Akhiezer functions and calculate the $N$-soliton solutions of the
noncommutative Toda hierarchy.


title:
Additive Nonparametric Reconstruction of Dynamical Systems from Time
  Series

abstract:
  We present a nonparametric way to retrieve a system of differential equations
in embedding space from a single time series. These equations can be treated
with dynamical systems theory and allow for long term predictions. We
demonstrate the potential of our approach for a modified chaotic Chua
oscillator.


title:
Scaling properties of growing noninfinitesimal perturbations in
  space-time chaos

abstract:
  We study the spatiotemporal dynamics of random spatially distributed
noninfinitesimal perturbations in one-dimensional chaotic extended systems. We
find that an initial perturbation of finite size $\epsilon_0$ grows in time
obeying the tangent space dynamic equations (Lyapunov vectors) up to a
characteristic time $t_{\times}(\epsilon_0) \sim b - (1/\lambda_{max}) \ln
(\epsilon_0)$, where $\lambda_{max}$ is the largest Lyapunov exponent and $b$
is a constant. For times $t < t_{\times}$ perturbations exhibit spatial
correlations up to a typical distance $\xi \sim t^z$. For times larger than
$t_{\times}$ finite perturbations are no longer described by tangent space
equations, memory of spatial correlations is progressively destroyed and
perturbations become spatiotemporal white noise. We are able to explain these
results by mapping the problem to the Kardar-Parisi-Zhang universality class of
surface growth.


title: Small and Large Scale Fluctuations in Atmospheric Wind Speeds

abstract:
  Atmospheric wind speeds and their fluctuations at different locations
(onshore and offshore) are examined. One of the most striking features is the
marked intermittency of probability density functions (PDF) of velocity
differences -- no matter what location is considered. The shape of these PDFs
is found to be robust over a wide range of scales which seems to contradict the
mathematical concept of stability where a Gaussian distribution should be the
limiting one. Motivated by the instationarity of atmospheric winds it is shown
that the intermittent distributions can be understood as a superposition of
different subsets of isotropic turbulence. Thus we suggest a simple stochastic
model to reproduce the measured statistics of wind speed fluctuations.


title: Introduction to Random Boolean Networks

abstract:
  The goal of this tutorial is to promote interest in the study of random
Boolean networks (RBNs). These can be very interesting models, since one does
not have to assume any functionality or particular connectivity of the networks
to study their generic properties. Like this, RBNs have been used for exploring
the configurations where life could emerge. The fact that RBNs are a
generalization of cellular automata makes their research a very important
topic. The tutorial, intended for a broad audience, presents the state of the
art in RBNs, spanning over several lines of research carried out by different
groups. We focus on research done within artificial life, as we cannot exhaust
the abundant research done over the decades related to RBNs.

categories: nlin.AO cond-mat.stat-mech cs.CC nlin.CG q-bio.MN q-bio.QM


title:
Entropy Maximization as a Holistic Design Principle for Complex Optimal
  Networks and the Emergence of Power Laws

abstract:
  We present a general holistic theory for the organization of complex
networks, both human-engineered and naturally-evolved. Introducing concepts of
value of interactions and satisfaction as generic network performance measures,
we show that the underlying organizing principle is to meet an overall
performance target for wide-ranging operating or environmental conditions. This
design or survival requirement of reliable performance under uncertainty leads,
via the maximum entropy principle, to the emergence of a power law vertex
degree distribution. The theory also predicts exponential or Poisson degree
distributions depending on network redundancy, thus explaining all three
regimes as different manifestations of a common underlying phenomenon within a
unified theoretical framework.

categories: nlin.AO cond-mat.stat-mech cs.IT math.IT q-bio.QM


title: Chaos induced coherence in two independent food chains

abstract:
  Coherence evolution of two food web models can be obtained under the stirring
effect of chaotic advection. Each food web model sustains a three--level
trophic system composed of interacting predators, consumers and vegetation.
These populations compete for a common limiting resource in open flows with
chaotic advection dynamics. Here we show that two species (the top--predators)
of different colonies chaotically advected by a jet--like flow can synchronize
their evolution even without migration interaction. The evolution is
charaterized as a phase synchronization. The phase differences (determined
through the Hilbert transform) of the variables representing those species show
a coherent evolution.


title: Open circular billiards and the Riemann hypothesis

abstract:
  A comparison of escape rates from one and from two holes in an experimental
container (e.g. a laser trap) can be used to obtain information about the
dynamics inside the container. If this dynamics is simple enough one can hope
to obtain exact formulas. Here we obtain exact formulas for escape from a
circular billiard with one and with two holes. The corresponding quantities are
expressed as sums over zeroes of the Riemann zeta function. Thus we demonstrate
a direct connection between recent experiments and a major unsolved problem in
mathematics, the Riemann hypothesis.


title: Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps

abstract:
  We report exact analytical expressions locating the $0\to1$, $1\to2$ and
$2\to4$ bifurcation curves for a prototypical system of two linearly coupled
quadratic maps. Of interest is the precise location of the parameter sets where
Naimark-Sacker bifurcations occur, starting from a non-diagonal period-2 orbit.
This result is the key to understand the onset of synchronization in networks
of quadratic maps.


title:
Structural Stability and Hyperbolicity Violation in High-Dimensional
  Dynamical Systems

abstract:
  This report investigates the dynamical stability conjectures of Palis and
Smale, and Pugh and Shub from the standpoint of numerical observation and lays
the foundation for a stability conjecture. As the dimension of a dissipative
dynamical system is increased, it is observed that the number of positive
Lyapunov exponents increases monotonically, the Lyapunov exponents tend towards
continuous change with respect to parameter variation, the number of observable
periodic windows decreases (at least below numerical precision), and a subset
of parameter space exists such that topological change is very common with
small parameter perturbation. However, this seemingly inevitable topological
variation is never catastrophic (the dynamic type is preserved) if the
dimension of the system is high enough.


title: Integrable Mappings Related to the Extended Discrete KP Hierarchy

abstract:
  We investigate self-similar solutions of the extended discrete KP hierarchy.
It is shown that corresponding ansatzes lead to purely discrete equations with
dependence on some number of parameters together with equations governing
deformations with respect to these parameters. Some examples are provided. In
particular, it is shown that the well known discrete first Painleve equation
(dPI) and its hierarchy arises as self-similar reduction of Volterra lattice
hierarchy which in turn can be treated as a reduction of the extended discrete
KP hierarchy. It is written down equations which naturally generalize dPI. It
is shown that theses discrete systems describe B\"acklund transformations of
Noumi-Yamada systems of type $A_{2(n-1)^{(1)}}$. We also consider Miura
transformations relating different infinite- and finite-field integrable
mappings. Simplest example of this kind of Miura transformations is given.


title:
Statistics of unstable periodic orbits of a chaotic dynamical system
  with a large number of degrees of freedom

abstract:
  For a simple model of chaotic dynamical systems with a large number of
degrees of freedom, we find that there is an ensemble of unstable periodic
orbits (UPOs) with the special property that the expectation values of
macroscopic quantities can be calculated using only one UPO sampled from the
ensemble. Evidence to support this conclusion is obtained by generating the
ensemble by Monte Carlo calculation for a statistical mechanical model
described by a space-time Hamiltonian that is expressed in terms of Floquet
exponents of UPOs. This result allows us to interpret the recent interesting
discovery that statistical properties of turbulence can be obtained from only
one UPO [G. Kawahara and S. Kida, J. Fluid Mech. {\bf 449}, 291 (2001); S. Kato
and M. Yamada, Phys. Rev. E {\bf 68}, 025302(R)(2003)].


title: Cell-centric heuristics for the classification of cellular automata

abstract:
  We study the classification of cellular-automaton update rules into Wolfram's
four classes. We start with the notion of the input entropy of a spatiotemporal
block in the evolution of a cellular automaton, and build on it by introducing
two novel entropy measures, one that is also based on inputs to the cells, the
other based on state transitions by the cells. Our two new entropies are both
targeted at the classification of update rules by parallel machines, being
therefore mindful of the necessary communications requirements; we call them
cell-centric input entropy and cell-centric transition entropy to reflect this
fact. We report on extensive computational experiments on both one- and
two-dimensional cellular automata. These experiments allow us to conclude that
the two new entropies possess strong discriminatory capabilities, therefore
providing valuable aid in the classification process.


title: Symbolic Codes for Rotational Orbits

abstract:
  Symbolic codes for rotational orbits and "islands-around-islands" are
constructed for the quadratic, area-preserving Henon map. The codes are based
upon continuation from an anti-integrable limit, or alternatively from the
horseshoe. Given any sequence of rotation numbers we obtain symbolic sequences
for the corresponding elliptic and hyperbolic rotational orbits. These are
shown to be consistent with numerical evidence. The resulting symbolic
partition of the phase space consists of wedges constructed from images of the
symmetry lines of the map.


title: Complex dynamics in a one--block model for earthquakes

abstract:
  A two-dimensional earthquake model that consists of a single block resting
upon a slowly moving rough surface and connected by two springs to rigid
supports is studied. Depending on the elastic anisotropy and the friction force
three generic regimes are possible: i) pure creep; ii) pure stick-slip motion;
and iii) a mixed regime. In all cases the long-time dynamics (fixed point,
periodic orbit or chaos) is determined by the direction of the pulling
velocity. The possible relevance of our findings to real faults is briefly
discussed.


title:
Routes to chaos in high-dimensional dynamical systems: A qualitative
  numerical study

abstract:
  This paper examines the most probable route to chaos in high-dimensional
dynamical systems in a very general computational setting. The most probable
route to chaos in high-dimensional, discrete-time maps is observed to be a
sequence of Neimark-Sacker bifurcations into chaos. A means for determining and
understanding the degree to which the Landau-Hopf route to turbulence is
non-generic in the space of $C^r$ mappings is outlined. The results comment on
previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss.


title: Relative Periodic Solutions of the Complex Ginzburg-Landau Equation

abstract:
  A method of finding relative periodic orbits for differential equations with
continuous symmetries is described and its utility demonstrated by computing
relative periodic solutions for the one-dimensional complex Ginzburg-Landau
equation (CGLE) with periodic boundary conditions. A relative periodic solution
is a solution that is periodic in time, up to a transformation by an element of
the equation's symmetry group. With the method used, relative periodic
solutions are represented by a space-time Fourier series modified to include
the symmetry group element and are sought as solutions to a system of nonlinear
algebraic equations for the Fourier coefficients, group element, and time
period. The 77 relative periodic solutions found for the CGLE exhibit a wide
variety of temporal dynamics, with the sum of their positive Lyapunov exponents
varying from 5.19 to 60.35 and their unstable dimensions from 3 to 8.
Preliminary work indicates that weighted averages over the collection of
relative periodic solutions accurately approximate the value of several
functionals on typical trajectories.


title: Periodic orbit theory and spectral rigidity in pseudointegrable systems

abstract:
  We calculate numerically the periodic orbits of pseudointegrable systems of
low genus numbers $g$ that arise from rectangular systems with one or two
salient corners. From the periodic orbits, we calculate the spectral rigidity
$\Delta_3(L)$ using semiclassical quantum mechanics with $L$ reaching up to
quite large values. We find that the diagonal approximation is applicable when
averaging over a suitable energy interval. Comparing systems of various shapes
we find that our results agree well with $\Delta_3$ calculated directly from
the eigenvalues by spectral statistics. Therefore, additional terms as e.g.
diffraction terms seem to be small in the case of the systems investigated in
this work. By reducing the size of the corners, the spectral statistics of our
pseudointegrable systems approaches the one of an integrable system, whereas
very large differences between integrable and pseudointegrable systems occur,
when the salient corners are large. Both types of behavior can be well
understood by the properties of the periodic orbits in the system.


title: Ultra-short pulses in linear and nonlinear media

abstract:
  We consider the evolution of ultra-short optical pulses in linear and
nonlinear media. For the linear case, we first show that the initial-boundary
value problem for Maxwell's equations in which a pulse is injected into a
quiescent medium at the left endpoint can be approximated by a linear wave
equation which can then be further reduced to the linear short-pulse equation.
A rigorous proof is given that the solution of the short pulse equation stays
close to the solutions of the original wave equation over the time scales
expected from the multiple scales derivation of the short pulse equation. For
the nonlinear case we compare the predictions of the traditional nonlinear
Schr\"odinger equation (NLSE) approximation which those of the short pulse
equation (SPE). We show that both equations can be derived from Maxwell's
equations using the renormalization group method, thus bringing out the
contrasting scales. The numerical comparison of both equations to Maxwell's
equations shows clearly that as the pulse length shortens, the NLSE
approximation becomes steadily less accurate while the short pulse equation
provides a better and better approximation.


title: Directed Chaotic Transport in Hamiltonian Ratchets

abstract:
  We present a comprehensive account of directed transport in one-dimensional
Hamiltonian systems with spatial and temporal periodicity. They can be
considered as Hamiltonian ratchets in the sense that ensembles of particles can
show directed ballistic transport in the absence of an average force. We
discuss general conditions for such directed transport, like a mixed classical
phase space, and elucidate a sum rule that relates the contributions of
different phase-space components to transport with each other. We show that
regular ratchet transport can be directed against an external potential
gradient while chaotic ballistic transport is restricted to unbiased systems.
For quantized Hamiltonian ratchets we study transport in terms of the evolution
of wave packets and derive a semiclassical expression for the distribution of
level velocities which encode the quantum transport in the Floquet band
spectra. We discuss the role of dynamical tunneling between transporting
islands and the chaotic sea and the breakdown of transport in quantum ratchets
with broken spatial periodicity.


title:
Divergence of the Chaotic Layer Width and Strong Acceleration of the
  Spatial Chaotic Transport in Periodic Systems Driven by an Adiabatic ac Force

abstract:
  We show for the first time that a {\it weak} perturbation in a Hamiltonian
system may lead to an arbitrarily {\it wide} chaotic layer and {\it fast}
chaotic transport. This {\it generic} effect occurs in any spatially periodic
Hamiltonian system subject to a sufficiently slow ac force. We explain it and
develop an explicit theory for the layer width, verified in simulations.
Chaotic spatial transport as well as applications to the diffusion of particles
on surfaces, threshold devices and others are discussed.


title: Extension of Moyal-deformed hierarchies of soliton equations

abstract:
  Moyal-deformed hierarchies of soliton equations can be extended to larger
hierarchies by including additional evolution equations with respect to the
deformation parameters. A general framework is presented in which the extension
is universally determined and which applies to several deformed hierarchies,
including the noncommutative KP, modified KP, and Toda lattice hierarchy. We
prove a Birkhoff factorization relation for the extended ncKP and ncmKP
hierarchies. Also reductions of the latter hierarchies are briefly discussed.
Furthermore, some results concerning the extended ncKP hierarchy are recalled
from previous work.


title: Hierarchical structure description of spatiotemporal chaos

abstract:
  We develop a hierarchical structure (HS) analysis for quantitative
description of statistical states of spatially extended systems. Examples
discussed here include an experimental reaction-diffusion system with
Belousov-Zhabotinsky kinetics, the two-dimensional complex Ginzburg-Landau
equation and the modified FitzHugh-Nagumon equation, which all show complex
dynamics of spirals and defects. We demonstrate that the spatial-temporal
fluctuation fields in the above mentioned systems all display the HS similarity
property originally proposed for the study of fully developed turbulence [Z.-S.
She and E. Leveque, Phys. Rev. Lett. {\bf 72}, 336 (1994)]. The derived values
of a HS parameter $\beta$ from experimental and numerical data in various
physical regimes exhibit consistent trends and characterize the degree of
turbulence in the systems near the transition, and the degree of heterogeneity
of multiple disorders far from the transition. It is suggested that the HS
analysis offers a useful quantitative description for the complex dynamics of
two-dimensional spatiotemporal patterns.


title:
A robust numerical method to study oscillatory instability of gap
  solitary waves

abstract:
  The spectral problem associated with the linearization about solitary waves
of spinor systems or optical coupled mode equations supporting gap solitons is
formulated in terms of the Evans function, a complex analytic function whose
zeros correspond to eigenvalues. These problems may exhibit oscillatory
instabilities where eigenvalues detach from the edges of the continuous
spectrum, so called edge bifurcations. A numerical framework, based on a fast
robust shooting algorithm using exterior algebra is described. The complete
algorithm is robust in the sense that it does not produce spurious unstable
eigenvalues. The algorithm allows to locate exactly where the unstable discrete
eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows
for stable shooting along multi-dimensional stable and unstable manifolds. The
method is illustrated by computing the stability and instability of gap
solitary waves of a coupled mode model.


title: On propagation failure in 1 and 2 dimensional excitable media

abstract:
  We present a non-perturbative technique to study pulse dynamics in excitable
media. The method is used to study propagation failure in one-dimensional and
two-dimensional excitable media. In one-dimensional media we describe the
behaviour of pulses and wave trains near the saddle node bifurcation, where
propagation fails. The generalization of our method to two dimensions captures
the point where a broken front (or finger) starts to retract. We obtain
approximate expressions for the pulse shape, pulse velocity and scaling
behavior. The results are compared with numerical simulations and show good
agreement.


title: On a 'Mysterious' Case of a Quadratic Hamiltonian

abstract:
  We show that one of the five cases of a quadratic Hamiltonian, which were
recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test,
fails to pass the Painleve test for integrability.


title: Nonlinear Dynamics in Psychophysiology - Importance of Time Scales

abstract:
  Presented theory of feelings and emotions is based on Nonlinear Dynamics and
Theory of Complex Systems. The most important assumption is that the brain may
be considered to be composed of subsystems characterized by different
characteristic time scales. The theory explains a possible role of feelings and
emotions in cognition. We propose to call presented theory Chaosensology.


title:
Spatial and temporal turbulent velocity and vorticity power spectra from
  sound scattering

abstract:
  By performing sound scattering measurements with a detector array consisting
of 62 elements in a flow between two counter-rotating disks we obtain the
energy and vorticity power spectra directly in both spatial and temporal
domains. Fast accumulated statistics and large signal-to-noise ratio allow to
get high quality data rather effectively and to test scaling laws in details.


title:
Time-independent approximations for periodically driven systems with
  friction

abstract:
  The classical dynamics of a particle that is driven by a rapidly oscillating
potential (with frequency $\omega$) is studied. The motion is separated into a
slow part and a fast part that oscillates around the slow part. The motion of
the slow part is found to be described by a time-independent equation that is
derived as an expansion in orders of $\omega^{-1}$ (in this paper terms to the
order $\omega^{-3}$ are calculated explicitly). This time-independent equation
is used to calculate the attracting fixed points and their basins of
attraction. The results are found to be in excellent agreement with numerical
solutions of the original time-dependent problem.


title: Lagrangian tracers on a surface flow: the role of time correlations

abstract:
  Finite time correlations of the velocity in a surface flow are found to be
important for the formation of clusters of Lagrangian tracers. The degree of
clustering characterized by the Lyapunov spectrum of the flow is numerically
shown to be in qualitative agreement with the predictions for the white-in-time
compressible Kraichnan flow, but to deviate quantitatively. For intermediate
values of compressibility the clustering is surprisingly weakened by time
correlations.


title: Two Component Kaup - Kupershmidt Equation

abstract:
  The Kaup - Kupershmidt equation is generalized to the system of equations in
the same manner as the Korteweg - de Vries equation is generalized to the
Hirota - Satsuma equation. The Gelfan - Dikii - Lax and Hamiltonian
formulatiohn for this generalization is given. The same construction is
repeated for the constrainded Kadomtsev - Pietviashvili - Lax operator what
leads to the forur component Kaup - Kupershmidt equation. The modified version
of the two component Kaup -Kupershmidt equation is presented and analysed.


title:
A model for urban growth processes with continuum state cellular
  automata and related differential equations

abstract:
  A new kind of cellular automaton (CA) for the study of the dynamics of urban
systems is proposed. The state of a cell is not described using a finite set,
but by means of continuum variables. A population sector is included, taking
into account migration processes from and towards the external world. The
transport network is considered through an integration index describing the
capability of the network to interconnect the different parts of the city. The
time evolution is given by Poisson distributed stochastic jumps affecting the
dynamical variables, with intensities depending on the configuration of the
system in a suitable set of neighbourhoods. The intensities of the Poisson
processes are given in term of a set of potentials evaluated applying fuzzy
logic to a practical method frequently used in Switzerland to evaluate the
attractiveness of a terrain for different land uses and the related rents. The
use of a continuum state space enables one to write a system of differential
equations for the time evolution of the CA and thus to study the system from a
dynamical systems theory perspective. This makes it possible, in particular, to
look systematically for bifurcations and phase transitions in CA based models
of urban systems.


title: A q-deformed nonlinear map

abstract:
  A scheme of q-deformation of nonlinear maps is introduced. As a specific
example, a q-deformation procedure related to the Tsallis q-exponential
function is applied to the logistic map. Compared to the canonical logistic
map, the resulting family of q-logistic maps is shown to have a wider spectrum
of interesting behaviours, including the co-existence of attractors -- a
phenomenon rare in one dimensional maps.


title:
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical
  Systems

abstract:
  We reinvestigate the dynamical behavior of a first order scalar nonlinear
delay differential equation with piecewise linearity and identify several
interesting features in the nature of bifurcations and chaos associated with it
as a function of the delay time and external forcing parameters. In particular,
we point out that the fixed point solution exhibits a stability island in the
two parameter space of time delay and strength of nonlinearity. Significant
role played by transients in attaining steady state solutions is pointed out.
Various routes to chaos and existence of hyperchaos even for low values of time
delay which is evidenced by multiple positive Lyapunov exponents are brought
out. The study is extended to the case of two coupled systems, one with delay
and the other one without delay.


title:
Transition from anticipatory to lag synchronization via complete
  synchronization in time-delay systems

abstract:
  The existence of anticipatory, complete and lag synchronization in a single
system having two different time-delays, that is feedback delay $\tau_1$ and
coupling delay $\tau_2$, is identified. The transition from anticipatory to
complete synchronization and from complete to lag synchronization as a function
of coupling delay $\tau_2$ with suitable stability condition is discussed. The
existence of anticipatory and lag synchronization is characterized both by the
minimum of similarity function and the transition from on-off intermittency to
periodic structure in laminar phase distribution.


title:
Localized Coherent Structures of Ishimori Equation I through Hirota's
  Bilinearization method:Time dependent/Stationary boundaries

abstract:
  Ishimori equation is a $(2+1)$ dimensional generalization of the $(1+1)$
dimensional integrable classical continuous Heisenberg ferromagnetic spin
equation. The richness of the coherent structures admitted by Ishimori equation
I such as dromion, lump and rationally- exponentially localized solutions, have
been demonstrated in the literature through $\bar \partial$ technique and
binary Darboux transformation method. To our knowledge Hirota's method had been
adopted to construct only the vortex solutions of Ishimori equation II. For the
first time, the various types of localized coherent structures mentioned above
have been constructed in this paper for the Ishimori equation I using the
Hirota's direct method. In particular we have brought out the significance of
boundaries and arbitrary functions in generating all these types of localized
structures and proved that the absence of such boundaries leads only to line
soliton solutions.


title: Generalized critical points analysis of acetylene vibrational dynamics

abstract:
  Classical tools of nonlinear dynamics are used to study the highly excited
vibrations of small molecules. For effective Hamiltonians with one polyad
number (approximate constant of motion), previously developed methods locate
new anharmonic modes using the critical points in the reduced classical phase
space. Theoretical arguments are given for generalizing the method to more than
one polyad number.
  The pure bending Hamiltonian of acetylene is analyzed to demonstrate the
effectiveness of critical points analysis. Four families of critical points are
born in distinct bifurcations, each corresponding to a novel anharmonic mode.
These modes are visualized with custom computer-generated animations.
  The same analysis is extended for the first time to the acetylene stretchbend
system, which has never been analyzed classically with all the resonance
couplings. Preliminary results are obtained for the polyad series containing
the C-H stretch overtones.


title: Stability and Diversity in Collective Adaptation

abstract:
  We derive a class of macroscopic differential equations that describe
collective adaptation, starting from a discrete-time stochastic microscopic
model. The behavior of each agent is a dynamic balance between adaptation that
locally achieves the best action and memory loss that leads to randomized
behavior. We show that, although individual agents interact with their
environment and other agents in a purely self-interested way, macroscopic
behavior can be interpreted as game dynamics. Application to several familiar,
explicit game interactions shows that the adaptation dynamics exhibits a
diversity of collective behaviors. The simplicity of the assumptions underlying
the macroscopic equations suggests that these behaviors should be expected
broadly in collective adaptation. We also analyze the adaptation dynamics from
an information-theoretic viewpoint and discuss self-organization induced by
information flux between agents, giving a novel view of collective adaptation.


title: Notes on information geometry and evolutionary processes

abstract:
  In order to analyze and extract different structural properties of
distributions, one can introduce different coordinate systems over the manifold
of distributions. In Evolutionary Computation, the Walsh bases and the Building
Block Bases are often used to describe populations, which simplifies the
analysis of evolutionary operators applying on populations. Quite independent
from these approaches, information geometry has been developed as a geometric
way to analyze different order dependencies between random variables (e.g.,
neural activations or genes).
  In these notes I briefly review the essentials of various coordinate bases
and of information geometry. The goal is to give an overview and make the
approaches comparable. Besides introducing meaningful coordinate bases,
information geometry also offers an explicit way to distinguish different order
interactions and it offers a geometric view on the manifold and thereby also on
operators that apply on the manifold. For instance, uniform crossover can be
interpreted as an orthogonal projection of a population along an m-geodesic,
monotonously reducing the theta-coordinates that describe interactions between
genes.


title:
Painleve property and the first integrals of nonlinear differential
  equations

abstract:
  Link between the Painleve property and the first integrals of nonlinear
ordinary differential equations in polynomial form is discussed. The form of
the first integrals of the nonlinear differential equations is shown to
determine by the values of the Fuchs indices. Taking this idea into
consideration we present the algorithm to look for the first integrals of the
nonlinear differential equations in the polynomial form. The first integrals of
five nonlinear ordinary differential equations are found. The general solution
of one of the fourth ordinary differential equations is given.


title:
Hiding message in Delay Time: Encryption with Synchronized time-delayed
  systems

abstract:
  We propose a new communication scheme that uses time-delayed chaotic systems
with delay time modulation. In this method, the transmitter encodes a message
as an additional modulation of the delay timeand then the receiver decodes the
message by tracking the delay time.We demonstrate our communication scheme in a
system of coupled logistic maps.Also we discuss the error of the transferred
message due to an external noiseand present its correction method.


title: ChaNoXity: The Nonlinear Dynamics of Nature

abstract:
  In this paper we employ the topological-multifuncoctional mathematical
language and techniques of non-injective illposedness developed earlier to
formulate a notion of ChaNoXity -- Chaos-Nonlinearity-Complexity -- in
describing the specifically nonlinear dynamical evolutionary processes of
Nature. Non-bijective ill-posedness is the natural mode of expression for
chanoxity that aims to focus on the nonlinear interactions generating dynamical
evolution of real irreversible processes. The basic dynamics is considered to
take place in a matter-antimatter kitchen space of Nature that is inaccessible
to both the functional matter and multifunctional antimatter components. These
component spaces are distinguished by opposing evolutionary directional arrows.
Dynamical equilibrium is considered to be represented by such competitively
collaborating stasis states of the matter-antimatter constituents of Nature.


title: Toward a Theory of Chaos

abstract:
  This paper formulates a new approach to the study of chaos in discrete
dynamical systems based on the notions of inverse ill-posed problems,
set-valued mappings, generalized and multivalued inverses, graphical
convergence of a net of functions in an extended multifunction space, and the
topological theory of convergence. Order, chaos, and complexity are described
as distinct components of this unified mathematical structure that can be
viewed as an application of the theory of convergence in topological spaces to
increasingly nonlinear mappings, with the boundary between order and complexity
in the topology of graphical convergence being the region in Multi(X) that is
susceptible to chaos. The paper uses results from the discretized spectral
approximation in neutron transport theory and concludes that the numerically
exact results obtained by this approximation of the Case singular eigenfunction
solution is due to the graphical convergence of the Poisson and conjugate
Poisson kernels to the Dirac delta and the principal value multifunctions
respectively. In Multi(X), the continuous spectrum is shown to reduce to a
point spectrum, and we introduce a notion of latent chaotic states to interpret
superposition over generalized eigenfunctions. Along with these latent states,
spectral theory of nonlinear operators is used to conclude that nature supports
complexity to attain efficiently a multiplicity of states that otherwise would
remain unavailable to it.


title:
Synchronization of Chaotic Oscillators due to Common Delay Time
  Modulation

abstract:
  We have found a synchronization behavior between two identical chaotic
systems^M when their delay times are modulated by a common irregular signal. ^M
  This phenomenon is demonstrated both in two identical chaotic maps whose
delay times are driven by a common^M chaotic or random signal and in two
identical chaotic oscillators whose delay times are driven by^M a signal of
another chaotic oscillator. We analyze the phenomenon by using^M the Lyapunov
exponents and discuss it in relation with generalized synchronization.^M


title: First experimental evidence for quantum echoes in scattering systems

abstract:
  A self-pulsing effect termed quantum echoes has been observed in experiments
with an open superconducting and a normal conducting microwave billiard whose
geometry provides soft chaos, i.e. a mixed phase space portrait with a large
stable island. For such systems a periodic response to an incoming pulse has
been predicted. Its period has been associated to the degree of development of
a horseshoe describing the topology of the classical dynamics. The experiments
confirm this picture and reveal the topological information.


title:
All-optical switching and amplification of discrete vector solitons in
  nonlinear cubic birefringent waveguide arrays

abstract:
  We study all-optical switching based on the dynamical properties of discrete
vector solitons in waveguide arrays. We employ the concept of the polarization
mode instability and demonstrate simultaneous switching and amplification of a
weak signal by a strong pump of the other polarization.


title: Energy spectra of developed superfluid turbulence

abstract:
  The spectrum of turbulence in superfluid liquid is modified by the nonlinear
energy dissipation caused by the mutual friction between quantized vortices and
the normal component of the liquid. In some region of two Reynolds parameters
characterizing the flow of a superfluid, we found the new state of the fully
developed turbulence. This state displays both the Kolmogorov-Obukhov
5/3-scaling law $E_k \propto k^{-5/3}$ and the new "3-scaling law" $E_k \propto
k^{-3}$, each in a well separated range of $k$.


title:
The effect of noise on the dynamics of a complex map at the
  period-tripling accumulation point

abstract:
  As shown recently (O.B.Isaeva et al., Phys.Rev E64, 055201), the phenomena
intrinsic to dynamics of complex analytic maps under appropriate conditions may
occur in physical systems. We study scaling regularities associated with the
effect of additive noise upon the period-tripling bifurcation cascade
generalizing the renormalization group approach of Crutchfield et al.
(Phys.Rev.Lett., 46, 933) and Shraiman et al. (Phys.Rev.Lett., 46, 935),
originally developed for the period doubling transition to chaos in the
presence of noise. The universal constant determining the rescaling rule for
the intensity of the noise in period-tripling is found to be
$\gamma=12.2066409...$ Numerical evidence of the expected scaling is
demonstrated.


title:
Allelomimesis as universal clustering mechanism for complex adaptive
  systems

abstract:
  Animal and human clusters are complex adaptive systems and many are organized
in cluster sizes $s$ that obey the frequency-distribution $D(s)\propto
s^{-\tau}$. Exponent $\tau$ describes the relative abundance of the cluster
sizes in a given system. Data analyses have revealed that real-world clusters
exhibit a broad spectrum of $\tau$-values, $0.7\textrm{(tuna fish
schools)}\leq\tau\leq 2.95\textrm{(galaxies)}$. We show that allelomimesis is a
fundamental mechanism for adaptation that accurately explains why a broad
spectrum of $\tau$-values is observed in animate, human and inanimate cluster
systems. Previous mathematical models could not account for the phenomenon.
They are hampered by details and apply only to specific systems such as cities,
business firms or gene family sizes. Allelomimesis is the tendency of an
individual to imitate the actions of its neighbors and two cluster systems
yield different $\tau$ values if their component agents display different
allelomimetic tendencies. We demonstrate that allelomimetic adaptation are of
three general types: blind copying, information-use copying, and non-copying.
Allelomimetic adaptation also points to the existence of a stable cluster size
consisting of three interacting individuals.


title: Managing Complexity

abstract:
  Physical analogs have shown considerable promise for understanding the
behavior of complex adaptive systems, including macroeconomics, biological
systems, social networks, and electric power markets. Many of today's most
challenging technical and policy questions can be reduced to a distributed
economic control problem. Indeed, economically-based control of large-scale
systems is founded on the conjecture that the price-based regulation (e.g.,
auctions, markets) results in an optimal allocation of resources and emergent
optimal system control. This paper explores the state of the art in the use
physical analogs for understanding the behavior of some econophysical systems
and deriving stable and robust control strategies for them. In particular we
review and discuss applications of some analytic methods based on a
thermodynamic metaphor according to which the interplay between system entropy
and conservation laws gives rise to intuitive and governing global properties
of complex systems that cannot be otherwise understood.


title:
Evaluating North American Electric Grid Reliability Using the
  Barabasi-Albert Network Model

abstract:
  The reliability of electric transmission systems is examined using a
scale-free model of network structure and failure propagation. The topologies
of the North American eastern and western electric networks are analyzed to
estimate their reliability based on the Barabasi-Albert network model. A
commonly used power system reliability index is computed using a simple failure
propagation model. The results are compared to the values of power system
reliability indices previously obtained using standard power system reliability
analysis methods, and they suggest that scale-free network models are useful
for estimating aggregate electric network reliability.


title:
On the complete integrability and linearization of certain second order
  nonlinear ordinary differential equations

abstract:
  A method of finding general solutions of second-order nonlinear ordinary
differential equations by extending the Prelle-Singer (PS) method is briefly
discussed. We explore integrating factors, integrals of motion and the general
solution associated with several dynamical systems discussed in the current
literature by employing our modifications and extensions of the PS method. In
addition to the above we introduce a novel way of deriving linearizing
transformations from the first integrals to linearize the second order
nonlinear ordinary differential equations to free particle equation. We
illustrate the theory with several potentially important examples and show that
our procedure is widely applicable.


title:
An unusual Li\'enard type nonlinear oscillator with properties of a
  linear harmonic oscillator

abstract:
  A Li\'enard type nonlinear oscillator of the form
$\ddot{x}+kx\dot{x}+\frac{k^2}{9}x^3+\lambda_1 x=0$, which may also be
considered as a generalized Emden type equation, is shown to possess unusual
nonlinear dynamical properties. It is shown to admit explicit nonisolated
periodic orbits of conservative Hamiltonian type for $\lambda_1>0$. These
periodic orbits exhibit the unexpected property that the frequency of
oscillations is completely independent of amplitude and continues to remain as
that of the linear harmonic oscillator. This is completely contrary to the
standard characteristic property of nonlinear oscillators. Interestingly, the
system though appears deceptively a dissipative type for $\lambda_1\leq0$ does
admit a conserved Hamiltonian description, where the characteristic decay time
is also independent of the amplitude. The results also show that the criterion
for conservative Hamiltonian system in terms of divergence of flow function
needs to be generalized.


title:
Stability and collisions of moving semi-gap solitons in Bragg
  cross-gratings

abstract:
  We report results of a systematic study of one-dimensional four-wave moving
solitons in a recently proposed model of the Bragg cross-grating in planar
optical waveguides with the Kerr nonlinearity; the same model applies to a
fiber Bragg grating (BG) carrying two polarizations of light. We concentrate on
the case when the system's spectrum contains no true bandgap, but only
semi-gaps (which are gaps only with respect to one branch of the dispersion
relation), that nevertheless support soliton families. Solely zero-velocity
solitons were previously studied in this system, while current experiments
cannot generate solitons with the velocity smaller than half the maximum group
velocity. We find the semi-gaps for the moving solitons in an analytical form,
and demonstrated that they are completely filled with (numerically found)
solitons. Stability of the moving solitons is identified in direct simulations.
The stability region strongly depends on the frustration parameter, which
controls the difference of the present system from the usual model for the
single BG. A completely new situation is possible, when the velocity interval
for stable solitons is limited not only from above, but also from below.
Collisions between stable solitons may be both elastic and strongly inelastic.
Close to their instability border, the solitons collide elastically only if
their velocities c1 and c2 are small; however, collisions between more robust
solitons are elastic in a strip around c1=-c2.


title: Lyapunov exponents from unstable periodic orbits in the FPU-beta model

abstract:
  In the framework of a recently developed theory for Hamiltonian chaos, which
makes use of the formulation of Newtonian dynamics in terms of Riemannian
differential geometry, we obtained analytic values of the largest Lyapunov
exponent for the Fermi-Pasta-Ulam-beta model (FPU-beta) by computing the time
averages of the metric tensor curvature and of its fluctuations along
analytically known unstable periodic orbits (UPOs). The agreement between our
results and the Lyapunov exponents obtained by means of standard numerical
simulations supports the fact that UPOs are reliable probes of a general
dynamical property as chaotic instability.


title:
Anomalous scaling of a passive scalar advected by the Navier--Stokes
  velocity field: Two-loop approximation

abstract:
  The field theoretic renormalization group and operator product expansion are
applied to the model of a passive scalar quantity advected by a non-Gaussian
velocity field with finite correlation time. The velocity is governed by the
Navier--Stokes equation, subject to an external random stirring force with the
correlation function $\propto \delta(t-t') k^{4-d-2\epsilon}$. It is shown that
the scalar field is intermittent already for small $\epsilon$, its structure
functions display anomalous scaling behavior, and the corresponding exponents
can be systematically calculated as series in $\epsilon$. The practical
calculation is accomplished to order $\epsilon^{2}$ (two-loop approximation),
including anisotropic sectors. Like for the well-known Kraichnan's rapid-change
model, the anomalous scaling results from the existence in the model of
composite fields (operators) with negative scaling dimensions, identified with
the anomalous exponents. Thus the mechanism of the origin of anomalous scaling
appears similar for the Gaussian model with zero correlation time and
non-Gaussian model with finite correlation time. It should be emphasized that,
in contrast to Gaussian velocity ensembles with finite correlation time, the
model and the perturbation theory discussed here are manifestly Galilean
covariant. The relevance of these results for the real passive advection,
comparison with the Gaussian models and experiments are briefly discussed.


title: Streams and Lazy Evaluation Applied to Integrable Models

abstract:
  Computer algebra procedures to manipulate pseudo-differential operators are
implemented to perform calculations with integrable models. We use lazy
evaluation and streams to represent and operate with pseudo-differential
operators. No order of truncation is needed since terms are produced on demand.
We give a series of concrete examples using the computer algebra language
MAPLE.


title: A normal form of thin fluid film equations provides initial conditions

abstract:
  We use dynamical systems theory to construct the normal form of the
Navier--Stokes equations for the flow of a thin layer of fluid upon a solid
substrate. The normal form equations illuminate the fluid dynamics by
decoupling the long-term flow of interest from the rapid viscous decay of the
transient shear modes. The normal form clearly shows the centre manifold of the
lubrication model and shows the result that the initial condition for the fluid
thickness of the lubrication model is \emph{not} the initial physical fluid
thickness, but instead is modified by the initial lateral shear flow. With
these initial conditions, better forecasts will be made using the lubrication
model. This dynamical systems approach will also enable similar illumination of
other complicated models of dynamics.