Volume 108, Number 4, November 2014
|Number of page(s)||6|
|Published online||13 November 2014|
Diffusion in randomly perturbed dissipative dynamics
1 Max Planck Institute for Mathematics in the Sciences - Inselstr. 22, 04103 Leipzig, Germany
2 Institute for Theoretical Physics, NSC KIPT - ul. Akademicheskaya 1, UA-61108 Kharkov, Ukraine
3 Institute for Complex Systems and Mathematical Biology, University of Aberdeen - Aberdeen AB24 3UE, UK
4 Queen Mary University of London, School of Mathematical Sciences - Mile End Road, London E1 4NS, UK
Received: 14 August 2014
Accepted: 23 October 2014
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.60.-k – Transport processes / 05.45.-a – Nonlinear dynamics and chaos
© EPLA, 2014
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