Cluster Synchronization of Coupled Genetic Regulatory Networks With Delays via Aperiodically Adaptive Intermittent Control

Abstract

In this paper, we study the cluster synchronization of coupled genetic regulatory networks with time-varying delays via aperiodically adaptive intermittent control on some nodes. The network is intermittently coupled and the intra-cluster coupling strength is adaptively adjusted. The graph of the coupling topology of each cluster is only required to have a directed spanning tree. Two cases of delays are considered. In the first case, by using the switching Lyapunov-based function and Razumikhin-type technique, the cluster synchronization criterion is presented which indicates that the cluster synchronization is realized via the aperiodically adaptive intermittent control. The second case is investigated by using the switching Lyapunov functional. Both the cluster synchronization criteria are established by the Linear Matrix Inequalities (LMIs), the lower bound of the aperiodical time span, and the maximum uncontrolled ratio. It is shown that the results are applicable to both the situations that the upper bound of the delay is larger and smaller than the lower bound of the aperiodical coupling and control width. Numerical simulations are carried out to illustrate the theoretical results.