The escape problem and stochastic resonance in a bistable system driven by fractional Gaussian noise

Abstract

In the present paper, for a symmetrical bistable system that is excited by a fractional Gaussian noise, via the examination upon the qualitative changes of the stationary probability densities, the phenomena of the noise induced transition and escape and the stochastic resonance, which is in the sense of that the particles oscillate between the double-well potential, are investigated. For a high noise intensity, the probability density function obtained by Monte Carlo method changes from bimodal to unimodal by decreasing the values of Hurst index H. However, in the low noise intensity regime the transition could not occur for all H. Based on numerical results we demonstrate the fact that the mean first passage time (MFPT) is dependent on the Hurst index H and the noise intensity D, and possesses an exponential form as T(D,H)=k1(H)exp⁡(k2(H)/D). In particular, with a higher noise intensity, T(D,H) represents itself as a monotonous increasing function of the MFPT with the increasing H, whereas it exhibits as a non-monotonic function of H in the low noise intensity regime. Finally, nonlinear response theory is applied to investigate the stochastic resonance induced by Hurst index H and noise intensity D, for which we find that only for low noise intensities the stochastic resonance exists via increasing Hurst index which means the effect of noise reduction. This phenomenon is quite different from the one of the classical case.