Stochastic resonance in a bistable system driven by weak periodic signal with multiple delays

The phenomenon of stochastic resonance in a bistable system with multiple delays is investigated. The analytic expression of approximation stationary probability density is obtained by using small delay approximation based on probability density approach. Numerical simulation is performed and it is shown that the analytic results are in good agreement with Monte Carlo simulation. Then the expression of the signal-to-noise (SNR) is derived by using two-state theory. Finally, the effect of multiple delays on SNR is discussed. It is found that the stochastic resonance phenomenon can be suppressed or promoted when multiple delays are increased.