Bistability induced by two cross-correlated Gaussian white noises

Abstract

A prototype model of a stochastic one-variable system with a linear restoring force driven by two cross-correlated multiplicative and additive Gaussian white noises was considered earlier [S. I. Denisov et al., Phys. Rev. E 68, 046132 (2003)]. The multiplicative factor was assumed to be quadratic in the vicinity of a stable equilibrium point. It was determined that a negative cross-correlation can induce nonequilibrium transitions. In this paper, we investigate this model in more detail and calculate explicit expressions of the stationary probability density. We construct a phase diagram and show that both additive and multiplicative noises can also generate bimodal probability distributions of the state variable in the presence of anti-correlation. We find the order parameter and determine that the additive noise has a disordering effect and the multiplicative noise has an ordering effect. We explain the mechanism of this bistability and specify its key ingredients.