Adaptive Event-Triggered Mechanism to Synchronization of Reaction–Diffusion CVNNs and Its Application in Image Secure Communication

This article is centered on the formulation of a refined adaptive sampled-data-based event-triggering control (ASDBETC) scheme for the synchronization of reaction–diffusion complex-valued neural networks (RDCVNNs) with probabilistic time-varying delays (TVDs). A refined ASDBETC mechanism is first proposed in a hierarchy structure, which differs from some conventional sampled-data-based event-triggering control mechanisms with preordained invariable threshold. The refined ASDBETC mechanism can adaptively adjust the orientation and frequency of event-triggered threshold parameters via the variational tendency of states and the corresponding Euclidean distance between states. Therefore, an intact bidirectional regulative mechanism that is sensitive to the changes of state is legitimately established to provide additional flexibility, which is conducive to better compromise between communication resources and control performance. Through considering the effect of uncertainties, the random TVDs belonging to two different intervals by a probabilistic form are introduced. Then, by leveraging a novel time-related Lyapunov–Krasovskii functional (LKF) that contains the more realistic sampled behaviors on the entire sampled interval, new synchronization conditions and controller design method are derived for RDCVNNs. Finally, the advantages of the refined ASDBETC strategy, the availability, and practicability of the developed theories are corroborated via two simulation examples.