Residence-times distribution function of bistable system subjected to noise recycling

In this paper, the residence-times distribution function (RTDF) is investigated theoretically and numerically in a prototypical bistable system subjected to noise recycling. Under the condition for adiabatic approximation, a theory is suggested by using a two-state model, based on which the escape rate is derived analytically and the RTDF has been obtained theoretically with a piecewise formula. Both the escape rate and the RTDF depend on not only the current state but also the earlier state. It is further demonstrated that the RTDF has displayed a feedback-induced structure due to the recycling procedure. Numerical simulations have been carried out, and good agreement could be found between the theory and the numerical results.