Global exponential synchronization of quaternion-valued memristive neural networks with time delays

Ruoyu Wei,Jinde Cao

doi:10.15388/namc.2020.25.15724

Abstract

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper.

Highlights

The memristor is considered to be the fourth fundamental circuit element, except resistor, capacitor, and inductor
As the extension of complex-valued memristive neural networks (CVNNs), the states, connection weights, and activation functions of quaternion-valued neural networks (QVNNs) are all in quaternion field
We focus on the drive-response global exponential synchronization of memristive QVNNs

Summary

Introduction

The memristor is considered to be the fourth fundamental circuit element, except resistor, capacitor, and inductor. Memristors has a special characteristic that it can remember its recent value between the period that the voltage is turned off and the time it turned on. As the extension of complex-valued memristive neural networks (CVNNs), the states, connection weights, and activation functions of QVNNs are all in quaternion field. To the best of our knowledge, the study of dynamical behavior of QVNNs mainly concentrate on the stability issue, the investigation of synchronization problem of QVNNs is still quite few, let alone the memristive QVNNs. Recently, some researchers introduced the memristive connection weights into CVNNs to construct a new model, which bring about some interesting results [39,46]. C(1)([−τ, 0], Rn) denotes the family of continuous functions from [−τ, 0] to Rn. co{F1, F2} denotes closure of the convex hull of Q produced by quaternion values F1, F2

Preliminaries and model formulation

Main results

Numerical examples

Conclusion