Study on exponential synchronisation between the time-delay spatiotemporal network and the target system

Abstract

In this paper, the problem of exponential synchronisation between time-delay spatiotemporal network and target system is studied. Based on the Lyapunov stability principle, the Lyapunov–Krasovskii generic function with exponential form is designed, and the form of the synchronisation controller is determined, so that the exponential synchronisation is realised between the time-delay spatiotemporal network and the target system. In simulation, Fisher–Kolmogorov system is further selected as the network node to verify the rationality of synchronisation scheme. This technology fully considers the effect of time delay on network synchronisation performance, making the synchronisation scheme more practical. In addition, exponential synchronisation technology can effectively adjust the rate of network synchronisation.