Noise induced order for skew-products over a non-uniformly expanding base

TL;DR

This paper demonstrates how adding noise to certain complex dynamical systems can suppress chaos, leading to more ordered behavior, especially in systems combining expanding and contracting dynamics.

Contribution

It establishes noise-induced order for a class of high-dimensional skew-product systems over non-uniformly expanding bases, extending previous results to more general settings.

Findings

Noise can suppress chaos in skew-product systems.

Order is induced in systems with non-uniformly expanding bases.

Results apply to systems with dimension greater than or equal to two.

Abstract

Noise-induced order is the phenomenon by which the chaotic regime of a deterministic system is destroyed in the presence of noise. In this manuscript, we establish noise-induced order for a natural class of systems of dimension $\geq 2$ consisting of a fiber-contracting skew product a over nonuniformly-expanding 1-dimensional system.