Transitions from deterministic to stochastic diffusion

Max Planck Institute for Physics of Complex Systems Nöthnitzer Str. 38, D-01187 Dresden, Germany

Corresponding author: rklages@mpipks-dresden.mpg.de

Received: 12 October 2001
Accepted: 9 January 2002

Abstract

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