Transitions from deterministic to stochastic diffusion

• Published in: Europhysics letters Vol. 57; no. 6; pp. 796 - 802
• Main Author: Klages, R
• Format: Journal Article
• Language: English
• Published: Les Ulis IOP Publishing 01.03.2002; EDP Sciences; EDP sciences
• Subjects: 05.40.Jc; 05.45.Ac; 05.60.Cd; Brownian motion; Classical chaos; Classical transport; Exact sciences and technology; Fluctuation phenomena, random processes, noise, and brownian motion; Low-dimensional chaos; Nonlinear dynamics and nonlinear dynamical systems; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Transport processes; Brownian motion; Low-dimensional system; Stochastic processes; Deterministic system; Modelling; Transport theory; Dynamical systems; Chaotic systems
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/epl/i2002-00581-4

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.