From Deterministic Chaos to Anomalous Diffusion
Abstract
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and dynamical entropies. The second part outlines the concept of deterministic diffusion. Then the escape rate formalism for deterministic diffusion, which expresses the diffusion coefficient in terms of the above two chaos quantities, is worked out for a simple map. Part three explains basics of anomalous diffusion by demonstrating the stochastic approach of continuous time random walk theory for an intermittent map. As an example of experimental applications, the anomalous dynamics of biological cell migration is discussed.
Cite
@article{arxiv.0804.3068,
title = {From Deterministic Chaos to Anomalous Diffusion},
author = {R. Klages},
journal= {arXiv preprint arXiv:0804.3068},
year = {2010}
}
Comments
49 pages, 20 figures; previous lecture notes extended by a new third chapter on anomalous diffusion; to be published in Reviews of Nonlinear Dynamics and Complexity, Vol.3, as a book chapter