2021/06/30 by Konstantinos Mamis, Mohammad Farazmand · 1 citation
Mathematics · Physics and Astronomy · #math.DS #nlin.PS #physics.comp-ph
paper · pdf · doi:10.1103/physreve.104.034201
published as Phys. Rev. E 104, 034201 (2021) · Minor revisions; In press in Phys. Rev. E
arxiv created 2021/08/10 · arxiv updated 2021/09/15
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.