Adaptive dynamic event-triggered cluster synchronization in an array of coupled neural networks subject to cyber-attacks

This paper is concerned with cluster synchronization in an array of coupled neural networks subject to cyber-attacks, where a random variable is employed to reflect the success ration of the launched cyber-attacks. To save the energy consumption and alleviate the transmission load of the network, a novel adaptive distributed dynamic event-triggered communication scheme is presented based on the local stochastic the state sampling information, compared with some existing results, the different event-triggered matrices and auxiliary variables are introduced for each node to adjust its threshold dynamically, which can further reduce the sampled-data transmission, the proposed event-triggered scheme includes some existing event-triggered schemes as special cases. The cluster synchronization controllers are designed based on the states of neighboring nodes at event-triggered instants, a new stochastic sampled-data dependent error model is constructed, some mean-square cluster synchronization criteria can be derived by the Lyapunov stability theory and algebraic graph theory, and the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the theoretical results.