Event-based cluster synchronization of coupled genetic regulatory networks

In this paper, the cluster synchronization of coupled genetic regulatory networks with a directed topology is studied by using the event-based strategy and pinning control. An event-triggered condition with a threshold consisting of the neighbors' discrete states at their own event time instants and a state-independent exponential decay function is proposed. The intra-cluster states information and extra-cluster states information are involved in the threshold in different ways. By using the Lyapunov function approach and the theories of matrices and inequalities, we establish the cluster synchronization criterion. It is shown that both the avoidance of continuous transmission of information and the exclusion of the Zeno behavior are ensured under the presented triggering condition. Explicit conditions on the parameters in the threshold are obtained for synchronization. The stability criterion of a single GRN is also given under the reduced triggering condition. Numerical examples are provided to validate the theoretical results.