Quasi-bipartite synchronization of a new stochastic impulsive reaction-diffusion network by self-triggered control approach

This note aims to develop a quasi-bipartite synchronization control strategy for stochastic reaction-diffusion networks via self-triggered control technology. Based on the information of past triggered moments of nodes, a new self-triggered impulsive controller is designed, and the Zeno behavior is avoided. The impulse control rate is proposed, and a self-triggered mechanism to determine the timing of impulses is provided, taking into account the Zeno behavior at the triggering moment, addressing practical challenges in fields such as mechanical engineering and aerial vehicles. On this basis, parameter mismatch and quasi-synchronization conditions of the network are fully considered, which can be applied to multi-node nonuniform synchronization systems. Furthermore, sufficient conditions and detailed proof process for quasi-bipartite synchronization of stochastic reaction-diffusion networks are provided. Finally, the correctness of the theoretical results of quasi-bipartite synchronization is verified by means of two numerical examples.