Noise induced bistability in a fluctuating environment

Bistability in some systems does not occur at the mean-field level but is induced by noise. In this work, we consider a system which exhibits bistability induced by noise but in the presence of environmental fluctuations. The system can transition between two environmental states at a specified rate. It has absorbing boundaries in one state and can switch between two metastable states in the other. At small values of a system parameter (epsilon), the model exhibits noise-induced switching behaviour and the probability distribution is bimodal which becomes unimodal at large values of epsilon. We calculate the exact eigenvalues and steady-state solutions of the system. We further extend the investigation by calculating the mean switching time between the two metastable states in the small parameter limit and compare its accuracy with simulation results.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This work investigates a bistable system induced by noise in the presence of environmental fluctuations. The system transitions between two environmental states at a specified rate and has absorbing boundaries in one state while switching between two metastable states in the other. The model exhibits noise-induced switching behavior at small values of a system parameter, with a bimodal probability distribution that becomes unimodal at large values of the parameter. The exact eigenvalues, steady-state solutions, and mean switching time between metastable states are calculated and compared with simulation results.