Cooperative mechanism of resonant behaviors in a fluctuating-mass generalized Langevin system with generalized Mittag–Leffler memory kernel

Abstract

In this study, we investigate the resonant behaviors in the fluctuating-mass generalized Langevin equation (GLE) with generalized Mittag–Leffler (M–L) memory kernel. By using the stochastic averaging method and Laplace transform, we obtain the exact expression of the first-order moment of system steady response, based on which we analyze the dynamical mechanism of the various non-monotonic phenomena. Based on tbe numerical results, we further discuss the dependence on various parameters systematically and study the interplay and cooperation between the generalized M–L memory kernel and trichotomous noise in terms of output amplitude amplification. The results reveal the coexistence of non-monotonic phenomena in the proposed system, such as bona fide stochastic resonance (SR), conventional SR and wide-sense SR. We even observe the stochastic multi-resonance (SMR) behaviors with five or six peaks in the evolution of output amplitude amplification varying with the driving frequency. It is worth emphasizing that quintuple-peak and sextuple-peak bona fide SR phenomena had never been observed in the previous literatures. Thus, these results will provide more extensive support for manipulating the resonant behaviors through system parameter control in the potential applications.