Resonant behavior of the generalized Langevin system with tempered Mittag-Leffler memory kernel

TL;DR

This paper investigates the resonant behaviors in a generalized Langevin system with tempered Mittag-Leffler memory, revealing how tempering and memory influence stochastic resonance through exact analytical expressions and simulations.

Contribution

It provides the first analytical expressions for stochastic resonance measures in a system with tempered Mittag-Leffler noise and explores the effects of tempering and memory parameters.

Findings

Temperament parameter significantly affects stochastic resonance.

Exact expressions for SR measures are derived.

Numerical simulations validate theoretical results.

Abstract

The generalized Langevin equation describes anomalous dynamics. Noise is not only the origin of uncertainty but also plays a positive role in helping to detect signal with information, termed stochastic resonance (SR). This paper analyzes the anomalous resonant behaviors of the generalized Langevin system with a multiplicative dichotomous noise and an internal tempered Mittag-Leffler noise. For the system with fluctuating harmonic potential, we obtain the exact expressions of several SR, such as, the first moment, the amplitude and the autocorrelation function for the output signal as well as the signal-noise ratio. We analyze the influence of the tempering parameter and memory exponent on the bona fide SR and the general SR. Moreover, it is detected that the critical memory exponent changes regularly with the increase of tempering parameter. Almost all the theoretical results are validated by numerical simulations.