Diffusion in randomly perturbed dissipative dynamics

Abstract

Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no longer invariant and there is the possibility of transport among them. Here we introduce a basic theoretical setting which enables us to study this hopping process from the perspective of anomalous transport using the concept of a random dynamical system with holes. We apply it to a simple model by investigating the role of hyperbolicity for the transport among basins. We show numerically that our system exhibits non-Gaussian position distributions, power-law escape times, and subdiffusion. Our simulation results are reproduced consistently from stochastic Continuous Time Random Walk theory.

References in corpus (6)

• Poincare recurrences and transient chaos in systems with leaks
• Universality of algebraic laws in Hamiltonian systems
• Recurrence Time Statistics for Finite Size Intervals
• Poincare recurrences from the perspective of transient chaos
• Escape from attracting sets in randomly perturbed systems
• Emerging attractors and the transition from dissipative to conservative dynamics