Event‐triggered synchronisation of Markovian reaction–diffusion inertial neural networks and its application in image encryption

This study investigates the issue of dissipative synchronisation for inertial neural networks with Markovian jumping parameters and reaction–diffusion terms via the event-based control strategy. First, for study convenience, by employing a suitable variable substitution, the original synchronisation error system is transformed to a first-order differential one, and then it is reformed as a compact form. Second, an innovative event-triggered communication scheme that consists of the system's state and its first-order derivatives is proposed, with which the current sampling signal is judged whether should be released. Third, by constructing a novel Lyapunov–Krasovskii functional, and integrating the reciprocally convex combination method, free-weighting matrix approach and Wirtinger-based integral inequality, the dissipative synchronisation criterion that has less conservatism is derived. Finally, two examples are provided, one is a simple numerical example to account for the effectiveness of the main results, the other realises the application of this study in establishing a spatiotemporal chaotic cryptosystem to transmit the encrypted image. Furthermore, the proposed cryptosystem has been illustrated to have obvious advantages of large key space and high security by simulation results.