In this paper, the problem of finite-time synchronisation of uncertain delay spatiotemporal networks via unidirectional coupling technology is investigated. Based on Lyapunov theorem and finite-time stability theory, an effective finite-time synchronisation scheme is designed to achieve finite-time synchronisation between uncertain delay spatiotemporal networks, and adaptive estimations of coupling coefficient, unknown parameter and uncertain network topology are realised. Then, the Fisher–Kolmogorov spatiotemporal model is used as the state equation of the network node for numerical simulation. The simulation results show that the finite-time synchronisation scheme is effective.

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.