Synchronization in Fixed Time for Reaction–Diffusion Quaternion-Valued NNs with Nonlinear Interconnected Protocol and Its Application

Abstract

This paper makes an interesting attempt to interconnect N quaternion-valued neural networks (QVNNs) with reaction-diffusion items by a nonlinear coupling protocol, which generates a meaningful issue of synchronization for the N subsystems. By designing a novel nonlinear feedback controller, the N subsystems can be synchronized in a fixed time, which is more efficient and practical than asymptotic synchronization. Based on the Lyapunov functional theory and fixed-time stability criterion, and by employing suitable inequality techniques, the fixed-time synchronization theorem of the nonlinear interconnected QVNNs with reactiondiffusion terms can be obtained. Furthermore, an application example that applies the main results to secure communication is provided, and the effectiveness and superiority of the proposed cryptosystem can be illustrated through comparisons.