Resonant behaviors of two coupled fluctuating-frequency oscillators with tempered Mittag-Leffler memory kernel

Abstract

The dynamics of coupled oscillators and their collective behaviors are of great significance in various fields. This paper explores the resonant behaviors in the system composed of two coupled fluctuating-frequency oscillators with tempered Mittag-Leffler (M-L) memory kernel. The study begins by demonstrating that the two particles synchronize in the long-time limit, indicating that the mean-field behavior aligns with that of each individual particle. Accordingly, we derive an exact analytical expression for the steady-state output amplitude gain (OAG) of the mean field using the stochastic average method. Furthermore, the research investigates the diverse phenomena of generalized stochastic resonance (GSR) and examines how various system parameters influence GSR. To validate the theoretical analysis, numerical simulations are conducted to support and verify our findings.