New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

Bingjun Li,Bingnan Tang

doi:10.1155/2021/9988073

Abstract

In the current work, we are devoted to the issue of uniform stability of fractional-order quaternion-valued neural networks involving discrete and leakage delays. Making use of the contracting mapping theory, we prove that the equilibrium point of the involved fractional-order quaternion-valued neural networks exists and is unique. Taking advantage of mathematical analysis strategy, a sufficient criterion involving delay to verify the global uniform stability for the considered fractional-order quaternion-valued neural networks is set up. Computer simulation figures are displayed to sustain the rationality of the established conclusions. This study generalizes and supplements the research of Xiu et al. (2020).

Highlights

It is public knowledge that that neural networks own broad application prospects in numerous aspects and many demesnes such as pattern recognition, artificial intelligence, graph manipulation, psychophysics, control engineering, bioscience, and so on [1,2,3]
Time delay usually arises in artificial neural networks and biological systems due to the time lag of signal transmission. e study shows that the time delay often brings about some unexpected dynamical phenomena such as loss of stability, periodic vibration, chaos, and so on [4]. us, it is an important task for us to reveal the influence of time delay on various dynamical phenomena in delayed neural networks
In 2019, Huang et al [7] set up a sufficient criterion to guarantee the existence of anti-periodic solutions and exponential stability for shunting inhibitory cellular neural networks involving proportional time delays by applying Lyapunov functional, inequality shills, and some mathematical analyses

Summary

Introduction

It is public knowledge that that neural networks own broad application prospects in numerous aspects and many demesnes such as pattern recognition, artificial intelligence, graph manipulation, psychophysics, control engineering, bioscience, and so on [1,2,3]. Jiang and Wang [18] studied the almost periodic solutions of delayed QVNNs. You et al [19] made a detailed analysis on the exponential stability of discrete-time quaternion-valued neural networks with leakage delay and discrete delays. This work will mainly focus on the following issues: (a) prove the existence and uniqueness of equilibrium point of fractional-order quaternion-valued neural networks; (b) set up the sufficient criterion to ensure global uniform stability of fractional-order quaternionvalued neural networks. A set of delay-dependent criteria to check the global uniform stability of system (2) is established In this present work, we modify system (2) as the following fractional-order quaternion-valued neural networks:.

Preliminaries and Assumptions

Existence and Uniqueness

Uniform Stability

Simulation Results

Conclusions