On the concept of complexity in random dynamical systems

Details On the concept of complexity in random dynamical systems On the concept of complexity in random dynamical systems

1995-05-12

arxiv.org/abs/cond-mat/9505054v1

Physics

Condensed Matter

35 pages, LaTeX

Scientific paper

10.1103/PhysRevE.53.2087

We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. The meaning of K is discussed in the context of the information theory, and it is shown that it can be determined from real experimental data. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent computed considering two nearby trajectories evolving under the same randomness. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical computations for noisy maps and sandpile models.

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