Stochastic resonance driven by two different kinds of colored noise in a bistable system

Abstract

The phenomenon of stochastic resonance in a bistable nonlinear system is investigated when both the multiplicative noise and the coupling between additive and multiplicative noise are colored with different values of noise correlation time ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}.$ Combining the functional analysis and unified colored noise approximation, the two different kinds of colored noise in the nonlinear system can be simplified. The signal-to-noise ratio is calculated when a weakly periodic signal is added to the system. It is found that there appears a transition between one peak and two peaks in the curve of the signal-to-noise ratio when either the noise correlation time ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ or the coupling strength \ensuremath{\lambda} between additive and multiplicative noise is increased. The transition between one and two peaks depending on ${\ensuremath{\tau}}_{1}$ and \ensuremath{\lambda} is more complex than that depending on ${\ensuremath{\tau}}_{2}.$