Event-Triggered Pinning Impulsive Control for Cluster Synchronization of Coupled Genetic Oscillator Networks With Proportional Delay

This article considers the cluster synchronization of coupled genetic oscillator networks (GONs) with proportional delay via the event-triggered pinning impulsive control (ETPIC). First, a novel Lyapunov-dependent event-triggered rule for impulsive functional differential equation that includes proportional delay is proposed by means of a new auxiliary function and the improved Lyapunov–Razumikhin method, which is different from the previous results. And then, a Lyapunov-dependent ETPIC rule is first designed, which integrates the pinning control with the established event-triggered impulsive control. On this basis, some new cluster synchronization criteria for coupled GONs with proportional delay are derived in the light of linear matrix inequalities. Note that the triggering impulsive instant is determined by the designed ETPIC rule, and only a fraction of nodes of each cluster are controlled at each triggering instant according to the designed algorithm. Finally, a numerical example is provided to show the effectiveness of the proposed approach.