Synchronization of Quaternion Valued Neural Networks with Mixed Time Delays Using Lyapunov Function Method

Abstract

This article is concerned with the fixed time synchronization for a class of Quaternion valued neural networks (QVNNs) with mixed time varying delays. Firstly, the QVNNs are separated into four equivalent real valued neural networks (RVNNs). Then, a novel suitable controller is designed to establish the fixed time synchronization of the QVNNs with the help of Lyapunov function. To give a glimpse, the finite time and fixed time stability definitions are proposed. Two different expressions of settling time are obtained by using two different lemmas. Finally, the validation of the theoretical results is shown through numerical simulation to a specific example.