Synchronization in Finite/Fixed Time of Delayed Discontinuous Reaction‐Diffusion Quaternion‐Valued Neural Networks

ABSTRACT In this paper, we study the issue of finite/fixed time synchronization (FFTS) analysis for delayed discontinuous quaternion‐valued neural networks (QVNNs) with diffusion effects. First, the influence produced by discontinuous activations is tackled by the theory of differential inclusion. Second, based on the Lyapunov stability theory and decomposition method, a novel negative exponent controller is designed to induce FFTS of the delayed discontinuous QVNNs with diffusion effects. Furthermore, we further investigate the finite‐time synchronization of the considered network system via the adaptive control scheme, and the upper‐bound of the settling time is explicitly estimated as well. The obtained theoretical results generalize and improve some existing outcomes on QVNNs. Finally, two numerical simulations are presented to verify the effectiveness and applicability of the developed theoretical results.