Control of spatiotemporal chaos by stochastic resetting

TL;DR

This paper investigates how stochastic resetting can control spatiotemporal chaos in dynamical systems by reducing chaos measures and inducing a phase transition, with validation through numerical simulations.

Contribution

It introduces a novel method of controlling chaos via stochastic resetting, identifying a critical rate that halts chaos spread in discrete maps and extending applicability to many-body systems.

Findings

Stochastic resetting reduces Lyapunov exponent and butterfly velocity.

A critical resetting rate causes a phase transition to chaos arrest.

Numerical simulations confirm theoretical predictions.

Abstract

We study how spatiotemporal chaos in dynamical systems can be controlled by stochastically returning them to their initial conditions. Focusing on discrete nonlinear maps, we analyze how key measures of chaos -- the Lyapunov exponent and butterfly velocity, which quantify sensitivity to initial perturbations and the ballistic spread of information, respectively -- are reduced by stochastic resetting. We identify a critical resetting rate that induces a dynamical phase transition, characterized by the simultaneous vanishing of the Lyapunov exponent and butterfly velocity, effectively arresting the spread of information. These theoretical predictions are validated and illustrated with numerical simulations of the celebrated logistic map and its lattice extension. Beyond discrete maps, our findings are applicable to virtually any chaotic extended classical many-body system.