Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker--Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time \tau on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time \tau can enhance stochastic resonance. Moreover, the longer the delay time \tau is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.