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

This paper studies the phenomenon of stochastic resonancein an asymmetric bistable system with time-delayed feedback andmixed periodic signal by using the theory of signal-to-noise ratioin the adiabatic limit. A general approximate Fokker--Planckequation and the expression of the signal-to-noise ratio are derivedthrough the small time delay approximation at both fundamentalharmonics and mixed harmonics. The effects of the additive noiseintensity $Q$, multiplicative noise intensity $D$, static asymmetry$r$ and delay time $tau$ on the signal-to-noise ratio arediscussed. It is found that the higher mixed harmonics and thestatic asymmetry $r$ can restrain stochastic resonance, and thedelay time $tau $ can enhance stochastic resonance. Moreover, thelonger the delay time $tau $ is, the larger the additive noiseintensity $Q$ and the multiplicative noise intensity $D$ are, whenthe stochastic resonance appears.