Switching event-triggered control for mean-square exponential synchronization of complex-valued delayed memristive neural networks under hybrid attacks

This paper investigates the mean-square exponential synchronization (MSES) of complex-valued delayed memristive neural networks (CVDMNNs) under complex-valued hybrid attacks. Considering the discontinuous right-hand sides of CVDMNNs, the systems are analyzed based on Filippov differential inclusion theory, and the interval matrix method is used to handle the memristive connection weights, thereby constructing error systems that are amenable to analysis. To utilize limited communication resources, a complex-valued switching event-triggered mechanism is introduced. Furthermore, to mitigate the effects of complex-valued hybrid attacks, consisting of complex-valued replay attacks and deception attacks following the Bernoulli distribution, a secure controller is designed that can simultaneously counteract the interference caused by residual terms in the error systems. On this basis, a piecewise Lyapunov functional is constructed, and the sufficient condition for achieving MSES under complex-valued hybrid attacks is derived using Lyapunov stability theory and inequality techniques. Based on the derived synchronization criterion, algorithms are proposed to determine the maximum allowable replay and deception attack rates of the system. Finally, a numerical example is provided to validate the effectiveness and superiority of the proposed scheme.