Exponential synchronization of Kuramoto-oscillator networks with stochastic disturbance under delayed impulsive control

Abstract

This paper investigates the synchronization problem of Kuramoto-oscillator networks (KONs) subject to random disturbances, utilizing delayed impulsive control. We address the challenge of stochastic impulsive delay by employing an average stochastic impulsive delay approach. Furthermore, we incorporate noise into the sinusoidal coupling process of KONs to achieve two key objectives: pth moment exponential synchronization and phase locking. The implementation of delayed impulsive control offers two significant advantages: flexibility in selecting the initial phase and the ability to choose a weak coupling strength between oscillators. This approach contrasts with traditional methods that often require strict initial conditions or strong coupling. Our theoretical framework provides a comprehensive solution to the synchronization problem in KONs under random disturbances. To demonstrate the practical applicability of our findings, we present two illustrative examples, validating the effectiveness of our proposed control strategy.