Mitigation of rare events in multistable systems driven by correlated noise

TL;DR

This paper presents a novel method to mitigate rare noise-induced transitions in multistable systems using time-delay feedback control, employing a new nonlinear Fokker-Planck approach for optimal parameter selection without extensive simulations.

Contribution

It introduces a parsimonious, simulation-free method for selecting control parameters to suppress rare events in multistable systems driven by correlated noise.

Findings

Effective mitigation of rare transitions demonstrated on optical laser model

Accurate prediction of modal drift and tail inflation achieved

Method avoids extensive Monte Carlo simulations

Abstract

We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen. We devise a parsimonious method for selecting the optimal control parameters, without requiring any Monte Carlo simulations of the system. This method relies on a new nonlinear Fokker-Planck equation whose stationary response distribution is approximated by a rapidly convergent iterative algorithm. In addition, our framework allows us to accurately predict, and subsequently suppress, the modal drift and tail inflation in the controlled stationary distribution. We demonstrate the efficacy of our method on two examples, including an optical laser model perturbed by multiplicative colored noise.