Noise Can Reduce Disorder in Chaotic Dynamics

TL;DR

This paper demonstrates that introducing weak noise into chaotic systems can reduce inhomogeneity among unstable periodic orbits, leading to a more ordered and regularized chaotic behavior, revealing a universal noise-induced ordering phenomenon.

Contribution

It uncovers a novel noise-induced ordering effect in chaotic dynamics, showing how weak noise regularizes the system by homogenizing the natural measure over unstable periodic orbits.

Findings

Weak noise reduces inhomogeneity of orbit weights.

Noise regularizes chaotic dynamics.

Effect is universal in deterministic chaos.

Abstract

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or natural measure) is generally highly inhomogeneous over the set, either diminishing or enhancing the contribution of these orbits into system dynamics. We show analytically and numerically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing impact, make a regularizing influence on the chaotic dynamics. This universal effect is rooted into the nature of deterministic chaos.