Exponential Synchronization of Reaction-Diffusion Systems on Networks via Asynchronous Intermittent Control

In this article, the exponential synchronization (ES) of the reaction-diffusion systems on networks is studied under an asynchronous aperiodic intermittent control strategy. Different from the preceding studies, the control strategy of each node is different, which is more general and challenging. Meanwhile, to address the asynchrony problem of the asynchronous intermittent control, a new asynchronous average control rate (ACR) is constructed, which is different for each node. The ACR is greater than the lower bound of the control rate in the existing literature, which makes the results of this article less conservative. Then, by constructing the Lyapunov function and adopting the graph theory, some ES criteria are given for the reaction-diffusion systems on networks. Finally, the effectiveness of the algorithms is verified by the numerical simulations.