Time-delayed feedback control of stochastic resonance induced by a multiplicative signal in a bistable system driven by cross-correlated noises

A linear time-delayed feedback is introduced into the bistable system driven by cross-correlated noises to control the stochastic resonance (SR) induced by the multiplicative periodic signal. The expression for the signal-to-noise ratio (SNR) of the system is derived in the small delay approximation and the adiabatic limit. By numerical computations, the effects of the delay time and strength of its feedback on the SNR are analyzed. The results indicate that the SR phenomenon can be enhanced or suppressed by adjusting the delay time and feedback strength. The influence of the time-delayed feedback on the SR depends not only on the sign of feedback strength, but also on the initial condition of the system. Moreover, both the delay time and the feedback strength can induce the critical behavior on the SR under given conditions.