Mittag-Leffler noise induced resonance behavior in a fractional generalized Langevin equation with random trichotomous inherent frequency

Abstract

The resonance behavior in a generalized Langevin equation and fractional generalized Langevin equation with random trichotomous inherent frequency and a generalized Mittag-Leffler noise are extensively investigated. An expression for the noise spectral of the generalized Mittag-Leffler noise is studied. Using the Shapiro–Loginov formula and Laplace transformation technique, exact expressions for the spectral amplification of generalized Langevin equation and fractional generalized Langevin equation are obtained. The simulation results turn out to show that the spectral amplification is a non-monotonic function of the characteristics of noise parameters and system parameters. In particular, the influence of generalized Mittag-Leffler noise is able to induce the generalized stochastic resonance phenomenon. The influence of the driving frequency is able to induce bona fide stochastic resonance and stochastic multi-resonance phenomena. It is found that the resonance behavior of the fractional generalized Langevin equation has more material results than that of the (non-fractional) generalized Langevin equation.