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 (ϵ), the model exhibits noise-induced switching behaviour and the probability distribution is bimodal which becomes unimodal at large values of ϵ. 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. •Extends noise induced bistable system to include environmental noise•Two environmental states: switching states in one and absorbing states in other•Eigenvalues and steady-state distribution is calculated analytically•Mean Switching Time is also calculated analytically•Provides a analytically tractable model with wide ranging applications