The relationship between stochastic resonance and coherence resonance in a bi-stable system

Abstract

The phenomenon of stochastic resonance (SR) and coherence resonance (CR) in a bi-stable system driven by additive and multiplicative noises has been investigated. For the case that the system has uncorrelated or correlated additive and multiplicative noises, we introduce an appropriate index that can characterize both SR and CR at the same time. Applying the first-order Euler numerical computation to study the SR and CR, We can show that for small noise density, with the increase of additive noise density, and the appearance of CR, if we add a small periodic force to the bi-stable system, SR will occur almost at the same time. However, with increasing multiplicative noise density, the above conclusion may be satisfied only for correlated additive and multiplicative noises. Moreover, the effects of other parameters on CR and SR can be shown to be the same.