Colored correlated multiplicative and additive Gaussian colored noises-induced transition of a piecewise nonlinear bistable model

Abstract

In this paper, we investigate the steady-state properties of a piecewise nonlinear bistable model driven by multiplicative and additive Gaussian colored noises with colored cross-correlation. Using the unified colored noise approximation, we derive the analytical expression of the steady-state probability density (SPD) function. Then the effects of colored correlated Gaussian colored noises on SPD are presented. According to the research results, it is found that there appear some new nonlinear phenomena in this system. The multiplicative colored noise intensity, the additive colored noise intensity and the cross-correlation strength between noises can induce the transition. However, the transition cannot be induced by the auto-correlation time of multiplicative and additive Gaussian colored noises as well as the cross-correlation time between noises.