Discrete Chaotic Systems Research Articles

DIRECTING ORBITS OF CHAOTIC DYNAMICAL SYSTEMS

In this paper, we consider the directing of orbits of discrete chaotic dynamical systems towards desired targets. Our aim is to significantly reduce the time needed to reach a target region by applying only small, bounded perturbations. We derive an open-loop control from methods of optimal control theory, and we discuss the effects of random dynamical noise on the open-loop control.

Diffusion in discrete nonlinear dynamical systems

Diffusive processes in one-dimensional discrete chaotic systems are considered. Drift and diffusion coefficients are calculated, which show critical behavior including logarithmic corrections. A Kubo formula for the diffusion coefficient in terms of the time-correlation function is given. Nondiffusive states may exist in certain parameter windows showing drift with broken symmetry or strict localization. Period-doubling bifurcations and states of periodic chaos describing chaotic but nondiffusive drift occur.