Complexity in Dynamical Systems with Noise

Abstract

We characterize the complexity in dynamical systems with a random perturbation by considering the rate $K$ of divergence of nearby orbits evolving under two different noise realizations. We discuss the meaning of $K$ in the context of the information theory and its physical relevance for the analysis of experimental data. Our definition of complexity becomes crucial for strongly intermittent systems where $K$ is very different from the Lyapunov exponent. This behavior is illustrated by some numerical computations.