Time-delayed feedback control for random dynamical systems

TL;DR

This paper extends time-delayed feedback control to random dynamical systems, demonstrating its effectiveness through applications to stochastic models and revealing noise-induced chaos transitions.

Contribution

It introduces a novel extension of TDFC for stochastic systems and classifies their behavior using Lyapunov exponents and fluctuations.

Findings

Noise-induced chaos triggers regime transitions.

Framework applicable to various stochastic models.

Lyapunov-based classification of random dynamics.

Abstract

We extend the Pyragas time-delayed feedback control (TDFC) to apply it to random dynamical systems and introduce an extended classification based on Lyapunov exponents and trajectory fluctuations. We demonstrate the applicability of this framework using the random logistic map and the stochastic R\"ossler system. Our results reveal that noise-induced chaos triggers a transition from stable to unstable regimes based on a phenomenon inherent to random dynamical systems.