Resonance dynamics evoked via noise recycling procedure

We study the effect of noise recycling on nonequilibrium escape dynamics in a bistable system. For small noise, the non-Markovian problem is reduced to a two-state model with the master equation depending on not only the current state but also the earlier state, based on which we are able to derive the analytical formulas for the switching rate, the autocorrelation function, and the power spectrum density (PSD). Both the theoretical and the numerical results show that, with modulating the time delay in noise recycling, a monotonic PSD may switch to a nonmonotonic one; the amplitude of PSD at resonance frequency exhibits a pronounced maximum at a certain noise level, declaring the onset of stochastic resonance (SR) in the absence of a weak periodic signal. Further, we also demonstrate that the linear response to the external periodic force displays a maximum at a certain level of time delay, displaying the signature of SR.