Tempered anomalous dynamics of globally coupled harmonic oscillators in the fluctuating potential field: stability, synchronism, and collective behaviors

The investigation of tempered anomalous dynamics holds great significance in many fields. In this study, we propose a model of globally coupled harmonic oscillators with tempered Mittag–Leffler (M–L) memory kernel in the fluctuating potential field. By analyzing the stationary-state output amplitude of mean field, we reveal the existence of rich generalized stochastic resonance phenomena of collective behaviors under stability conditions. Moreover, we find that the system can achieve asymptotic synchronism under a more relaxed condition. Through numerical simulations, we verify the analytical results and discuss the impact of system parameters on collective behaviors. Additionally, by introducing the concepts of mean first stabilization time and mean first synchronization time, we delve deeper into the asymptotic process of system stabilization/synchronization and clearly observe the existence of noise-enhanced stabilization and synchronization.