Stochastic resonance of an asymmetric tristable system driven by cross-correlated Ornstein–Uhlenbeck noise

Abstract

Stochastic resonance of an asymmetric tristable system driven by a periodic forcing and cross-correlated Ornstein–Uhlenbeck (O–U) noise is investigated. An approximate Fokker-Planck Equation for an asymmetric tristable system driven by a periodic forcing and cross-correlated O–U noise is derived in the adiabatic limit by using the unified colored-noise approximation method and the stochastic equivalent rules. Afterwards, the expression for spectral amplification (SA), the stationary probability density function (PDF) and the mean first passage time (MFPT) are derived. By considering the influence of asymmetric potential function and cross-correlated noise, the phenomenon of noise enhancing stability (NES) and stochastic resonance (SR) can be found. It can also be found that the response of the tristable system can be effectively improved by properly selecting the relevant noise intensity and the asymmetric constant. This proves the excellent performance of the system, and provides a good theoretical support for practical engineering application.