Secure synchronization of semi‐Markov jump interconnected reaction—diffusion neural networks under stochastic cyber‐attacks via pointwise control strategy

Abstract This article investigates the secure synchronization of semi‐Markov jump interconnected neural networks (s‐MJINNs) with reaction—diffusion terms subject to stochastic cyber‐attacks. The switching of the system's parameters is characterized by a semi‐Markov process, while the communication topology is assumed to be perturbed by Bernoulli‐distributed stochastic cyber‐attacks. In addition, a pointwise control scheme is adopted to minimize control costs and facilitate implementation. Based on the Lyapunov method, the Laplacian matrix, and employing inequality techniques including Jensen's and Young's inequality, sufficient synchronization criteria in terms of linear matrix inequalities are obtained to ensure that synchronization is achieved between the subsystems. Finally, an example is provided to demonstrate the effectiveness of and application potential in secure communications.