Adaptive protocol-based control for reaction-diffusion memristive neural networks with semi-Markov switching parameters

This study explores the asynchronous control of reaction -diffusion memristive neural networks (RDMNNs) using an innovative adaptive event -triggered protocol. The unique characteristic of RDMNNs is captured through a semi-Markov process model, wherein the probability density function of the duration time is contingent on two consecutive modes. A novel adaptive eventtriggered strategy, specifically designed for the semi-Markov switching signal, is introduced to effectively reduce the network's bandwidth usage. The determination of thresholds in the adaptive triggering criterion is intricately associated with the system state residuals. Due to the mismatch between the controller and the RDMNNs, the protocol -based controller operates asynchronously. This asynchronous operation is characterized by a hidden semi-Markovian model. Utilizing stochastic Lyapunov functions that correlate with the detected and system modes, several sufficient criteria for designing an effective asynchronous controller are provided, thereby ensuring the stochastic stability of the system. Finally, the feasibility of the proposed scheme is validated through a simulated example.