Hasil untuk "nlin.CD"

N. V. Kuznetsov, T. N. Mokaev

For the Rössler system we verify Eden's conjecture on the maximum of local Lyapunov dimension. We compute numerically finite-time local Lyapunov dimensions on the Rössler attractor and embedded unstable periodic orbits. The UPO computation is done by Pyragas time-delay feedback control technique.

D. Dmitrishin, E. Franzheva, A. Stokolos

In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of detecting T-cycles. Some numerical simulations are presented.

Xiao-Song Yang

In this paper targetability of chaotic sets with small controls is discussed by virtue of some results of geometric control theory. It is proved that given a chaotic set Λ, it is possible to steer a orbit in to every final state in some neighborhood of the chaotic set by suitable small perturbations to the parameters of the system under the Lie rank condition.

E. M. Shahverdiev, K. A. Shore

Secure chaos based multiplex communication system scheme is proposed utilizing globally coupled semiconductor lasers with multiple variable time delay optoelectronic feedbacks.

Itamar Procaccia, K. R. Sreenivasan

We present a personal view of the state of the art in turbulence research. We summarize first the main achievements in the recent past, and then point ahead to the main challenges that remain for experimental and theoretical efforts.

Manuele Santoprete

We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak anisotropy. In particular we find that the symmetric periodic orbits of the Manev system are perturbed to periodic orbits in the anisotropic problem.

Yu. Dabaghian

A cycle expansion technique for discrete sums of several PF operators, similar to the one used in standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an interesting universal behavior, which illustrates the details of the interference between the particlar mappings entering the sum.

Guillaume Bal, George Papanicolaou, Leonid Ryzhik

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

M. A. Jafarizadeh, S. Behnia

Hierarchy of one and many-parameter families of random trigonometric chaotic maps and one-parameter random elliptic chaotic maps of $\bf{cn}$ type with an invariant measure have been introduced. Using the invariant measure (Sinai-Ruelle-Bowen measure), the Kolmogrov-Sinai entropy of the random chaotic maps have been calculated analytically, where the numerical simulations support the results

A. J. Roberts

Centre manifold techniques are used to derive rationally a description of the dynamics of thin films of fluid. The derived model is based on the free-surface $η(x,t)$ and the vertically averaged horizontal velocity $\avu(x,t)$. The approach appears to converge well and has significant differences from conventional depth-averaged models.

H. Kantz, T. Schreiber

We derive a locally projective noise reduction scheme for nonlinear time series using concepts from deterministic dynamical systems, or chaos theory. We will demonstrate its effectiveness with an example with known deterministic dynamics and discuss methods for the verification of the results in the case of an unknown deterministic system.

C. Chandre, H. R. Jauslin

We review a formulation of a renormalization-group scheme for Hamiltonian systems with two degrees of freedom. We discuss the renormalization flow on the basis of the continued fraction expansion of the frequency. The goal of this approach is to understand universal scaling behavior of critical invariant tori.

Giorgio Mantica

An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling relations for the average complexity of symbolic trajectories are formally the same as those governing the semi-classical limit of quantum systems. Two cases-the circle, and the stadium-are examined in detail, and are presented as paradigms.

E. M. Shahverdiev

We investigate synchronization between two unidirectionally coupled chaotic multi-feedback Ikeda systems and find both the existence and stability conditions for anticipating, lag, and complete synchronizations.Generalization of the approach to a wide class of nonlinear systems is also presented.

Sandro Wimberger, Andreas Buchleitner

A statistical analysis of the ionization yield of one-dimensional, periodically driven hydrogen Rydberg states is provided. We find excellent agreement with predictions for the conductance across an Anderson-localized, quasi one-dimensional, disordered wire, in the semiclassical limit of highly excited atomic initial states.

Vladimir Gudkov, Joseph E. Johnson

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

Alexander Loskutov, Alexei Ryabov

A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are investigated. In the phase plane areas corresponding to decrease and increase of the velocity of billiard particles are found. Average velocities of the particle ensemble as functions of the number of collisions are obtained.

Arul Lakshminarayan

Relaxation in the time correlation between operators is studied. Quantized chaotic systems are shown to have distinct relaxation fluctuations that are universal and can be usefully modelled by Random Matrix Theory. Various quantized maps are used to demonsrate these results.

Thomas Schreiber, Andreas Schmitz

We propose a general scheme to create time sequences that fulfill given constraints but are random otherwise. Significance levels for nonlinearity tests are as usually obtained by Monte Carlo resampling. In a new scheme, constraints including multivariate, nonlinear, and nonstationary properties are implemented in the form of a cost function.

T. Schreiber, H. Kantz

We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the real time extraction of the fetal electrocardiogram from abdominal recordings.