Exponential synchronization of quaternion‐valued memristor‐based neural networks with time‐varying delays

Abstract

Summary In this paper, the global exponential synchronization of quaternion‐valued memristor‐based neural networks with time‐varying delays is discussed. Firstly, by using the differential inclusion theory and the set‐valued map theory, the discontinuous quaternion‐valued memristive neural networks is transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With the ω$$ \omega $$‐measure method and Halanay inequality, the criterion for global exponential synchronization of the quaternion‐valued memristive neural networks is given. At last, a numerical simulation is given to prove the validity of the main results.

Adaptive Global Synchronization for a Class of Quaternion-Valued Cohen-Grossberg Neural Networks with Known or Unknown Parameters

“…Therefore, studying the dynamic characteristics of QVNNs is a challenging topic. Recently, many results such as the µ-stability [12,13], stability [14][15][16][17][18], anti-synchronization [19,20], and synchronization [21][22][23][24][25][26] of QVNNs have been reported. However, to the best of our knowledge, there are few reports on the dynamic characteristics of QVCGNNs in the literature.…”

“…Synchronization involves coupled systems reaching identical dynamical behaviors at the same time. Since the synchronization of two chaotic systems was first achieved in 1990 by Pecora and Carrol [27] using the drive-response method, chaos synchronization began to enter the field of vision of researchers.To solve the synchronization problem, scholars have designed many control methods and obtained various outcomes [19][20][21][22][23][24][25][26][28][29][30][31][32]. Based on the Lyapunov stability theory and introducing a new definition for global quasi-synchronization, refs.…”

“…For memristive neural networks (MNNs), Ref. [22,26] designed different controllers to explore fixed-time synchronization in a quaternion field. Through dividing the model into equivalent real-valued systems, utilizing fixed-time theory, and constructing novel nonlinear feedback controllers, fixed-time synchronization of a neural network with delays was investigated in [23].…”