Space-Dividing-Based Cluster Synchronization of Reaction-Diffusion Genetic Regulatory Networks via Intermittent Control

Abstract

In this paper, we focus on the cluster synchronization of reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays, where the state of the system is not only time-dependent but also spatially-dependent due to the presence of the reaction-diffusion terms. First, we construct an intermittent space-dividing controller that effectively combines the two control strategies, making it more cost-effective. Furthermore, based on the activation function division approach, we propose a regulation function division method that can improve the delay upper bound of RDGRNs; meanwhile, the cluster synchronization criteria of RDGRNs under the proposed controller are derived based on the Lyapunov theory and Halanay's et al. inequality techniques. Finally, the criteria's effectiveness is demonstrated by numerical examples of the system in one- and two-dimensional space.