Synchronization resilience of coupled fluctuating-damping oscillators in small-world weighted complex networks

The mechanisms of synergy in complex networks have garnered significant attention across scientific disciplines. In this paper, we present a model of coupled oscillators with damping fluctuations within a small-world weighted complex network. We analyze the system’s asymptotic synchronization to derive conditions for asymptotic stability and evaluate the steady-state response. Our numerical simulations highlight the substantial impact of network weight heterogeneity and scale on asymptotic synchronization. We also examine asymptotic synchronization resilience under various removal strategies, revealing that increased noise intensity and lower switching rates reduce resilience. Notably, the removal of strong links poses the greatest vulnerability, while weak links have minimal impact. Interestingly, enhancing weight heterogeneity and scale can improve resilience in certain cases. Our results further show that heterogeneity accelerates synchronization speed, indicating a non-monotonic relationship with network scale. Ultimately, we confirm our theoretical findings and reveal intriguing generalized stochastic resonance (GSR) phenomena.