Bistability induced by two cross-correlated Gaussian white noises

TL;DR

This paper explores how cross-correlated Gaussian white noises can induce bistability in a stochastic system, providing explicit probability densities, phase diagrams, and insights into the effects of additive and multiplicative noises.

Contribution

It extends previous work by deriving explicit stationary distributions, constructing phase diagrams, and elucidating the mechanisms behind noise-induced bistability.

Findings

Negative cross-correlation induces nonequilibrium transitions.

Both additive and multiplicative noises can generate bimodal distributions.

Additive noise tends to disorder, while multiplicative noise tends to order the system.

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.