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.

本文研究时空时空网络与目标系统之间的指数同步问题。根据Lyapunov稳定性原理，设计了具有指数形式的Lyapunov–Krasovskii泛型函数，并确定了同步控制器的形式，从而实现了时空时空网络与目标系统之间的指数同步。在仿真中，进一步选择Fisher–Kolmogorov系统作为网络节点，以验证同步方案的合理性。该技术充分考虑了时延对网络同步性能的影响，使同步方案更加实用。另外，指数同步技术可以有效地调整网络同步速率。