Noise-induced order in high dimensions

TL;DR

This paper explores how noise affects high-dimensional dynamical systems, revealing complex phenomena like coexistence of chaos and order that challenge traditional concepts of noise-induced behavior.

Contribution

It provides the first detailed analysis of noise-induced phenomena in high-dimensional systems, showing coexistence of chaos and order.

Findings

Increase in positive Lyapunov exponents with noise

Emergence of characteristic periods due to noise

Change in Kolmogorov--Sinai entropy with noise

Abstract

Noise-induced phenomena in high-dimensional dynamical systems were investigated from a random dynamical systems point of view. In a class of generalized H\'enon maps, which are randomly perturbed delayed logistic maps, with monotonically increasing noise levels, we observed (i) an increase in the number of positive Lyapunov exponents from 4 to 5, and the emergence of characteristic periods at the same time, and (ii) a decrease in the number of positive Lyapunov exponents from 4 to 3, and an increase in Kolmogorov--Sinai entropy at the same time. Our results imply that simple concepts of noise-induced phenomena, such as noise-induced chaos and/or noise-induced order, may not describe those analogue in high dimensional dynamical systems, owing to coexistence of noise-induced chaos and noise-induced order.