In this paper we give an example of a real-analytic Hamiltonian system whose restrictions onto different energy levels are Anosov flows for E > Ecr, have only transitive trajectories for E = Ecr and are analytically integrable for E < Ecr where E|mathrmcr is some critical level of energy. This gives a simple example of a transition from chaos to integrability (on a fixed energy level) via a pas...

Space-time variational formulations and adaptive Wiener–Hermite polynomial chaos Galerkin discretizations of Kolmogorov equations in infinite dimensions, such as Fokker–Planck andOrnstein–Uhlenbeck equations for functions defined on an infinite-dimensional separable Hilbert space H , are developed. The wellposedness of these equations in the Hilbert space L2(H, μ) of functions on the infinite-d...

G.Geetha Professor and Head, Division of Research and Development Lovely Professional University, Phagwara, India [email protected] Abstract We propose the fractal generation method to generate the different types of fractals using chaos theory. The fractals are generated by Iterated Function System (IFS) technique. The chaos theory is an unpredictable behavior arises in the dynamical system...

In this paper, we propose a simple method for chaos synchronization in discrete-time, based on new criterion for stability. This criterion implying the Lyapunov stabilization criterion, and is applicable to some typical chaotic systems. Keywords: Chaos synchronization, dynamical systems, new criterion, discrete-time, Lyapunov stability 1 Introduction During the last decade, synchronization of c...

It is shown that when certain conditions are met, the random dynamics of radiation in a ring cavity containing a nonlinear element can be described by means of a 2-D representation with a rapidly oscillating exponential. Such a representation generates strong mixing in the attracting region of the phase space and is equivalent to a certain random representation when the exciting signal contains...

We examine the sensitiveness of the free-energy landscape of a directed polymer in random media with respect to various kinds of infinitesimally weak perturbation including the intriguing case of temperature chaos. To this end, we combine the replica Bethe Ansatz approach outlined by Sales and Yoshino (e-print cond-mat/0112384), the mapping to a modified Sinai model, and numerically exact calcu...

Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated....

A non-vanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system, however no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ε = E/N , the energy per degree of freedom. The fu...

human intervention in intensification of natural hazards is a concern for researchers. recognizing the response of morphological phenomena to human activities is not traceable in all phenomena. small landforms could capture short-term changes caused by human interventions and react to them. playa are among the areas in which micro-landforms changes can be traced monthly or permanently. playa ar...