Slow Stochastic Switching by Collective Chaos of Fast Elements

TL;DR

This paper investigates how slow variables in coupled slow-fast systems exhibit stochastic switching driven by collective chaos of fast elements, revealing complex dependence on timescale ratios and broad applicability.

Contribution

It introduces the concept of adiabatic kinetic branches and demonstrates stochastic switching mediated by collective chaos in slow-fast dynamical systems.

Findings

Switching over adiabatic kinetic branches occurs in slow-fast systems.

Switching frequency depends nonlinearly on the timescale ratio.

The phenomena are widespread in slow-fast dynamical systems.

Abstract

Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic limit. The dynamics without the limit are found to be represented by stochastic switching over these branches mediated by the collective chaos of the fast elements, while the switching frequency shows a complicated dependence on the ratio of the two timescales with some resonance structure. The ubiquity of the phenomena in the slow--fast dynamics is also discussed.