Stochastic systems with cross-correlated Gaussian white noises

Abstract

This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises. Both steady state properties of the stochastic nonlinear systems and the nonequilibrium transitions induced by the crosscorrelated noises are studied. The stationary solutions of the Fokker-Planck equation for three specific examples are analysed. It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.

Realising the decomposition of a multi‐frequency signal under the coloured noise background by the adaptive stochastic resonance in the non‐linear system with periodic potential

“…In most studies, the Gaussian white noise is usually added in signals to simulate a noisy background [18]. However, the noise of the realistic model may be in the coloured noise form [19][20][21][22][23][24][25].…”