Dissipative Synchronization of Semi-Markov Jump Reaction–Diffusion Complex Dynamical Networks via Adaptive Event-Triggering

This work addresses the dissipative synchronization for complex dynamical networks (CDNs) with semi-Markov jump parameters under adaptive event-triggering. Due to the complexity of network environment, a semi-Markov process (SMP) is introduced into the system modeling. The adaptive event-triggering protocol (AETP) is developed to dynamically adjust the triggering threshold based on the synchronization error, which significantly reduces unnecessary data transmissions and avoids Zeno behavior by guaranteeing a positive inter-event interval. Subsequently, a nonfragile controller is designed for potential fluctuations in controller gain. By constructing Lyapunov–Krasovskii functional (LKF) and employing advanced integral inequalities, sufficient synchronization conditions are derived to ensure that the CDNs achieve stochastic stability with strictly dissipative characteristic. Simulation results demonstrate the effectiveness of the proposed control scheme.