On Pseudo Almost Automorphic Solutions to Quaternion-Valued Cellular Neural Networks With Delays

Changjin Xu

doi:10.1109/access.2020.2964039

Abstract

This manuscript considers quaternion-valued cellular neural networks with delays. Applying pseudo almost automorphic solution theory of delayed differential equations and pertinent inequalities, a new sufficient criterion to guarantee the existence and global exponentially stability of pseudo almost automorphic solutions of quaternion-valued cellular neural networks with delays are presented. Different from Xiang and Li, no assumption for kernel functions is necessary. Simulation results is displayed to verify the validity of theoretical analyses. Up to now, few scholars have dealt with this aspect. The obtained results of this manuscript are completely new and complement some previous studies to a certain extent.

Highlights

As is known to us, the dynamical property of cellular neural networks has attracted great attention of scholars from all over the world since cellular neural networks can be successfully applied to various areas such as image processing, associative memories, artificial intelligence, disease diagnosis and so on [1]–[16]
Wang et al [21] investigated the periodic solution of cellular neural networks; Li and Wang [22] studied the almost periodic solutions to a class of cellular neural networks; Xu and Li [23] discussed the anti-periodic solutions for cellular neural networks; Aouiti et al [24] analyzed the stability of piecewise pseudo almost periodic solution for delayed inertial neural networks; Liu [25] focused on the pseudo almost periodic solutions for cellular neural networks with leakage delays; Abbas et al [26] made a detailed analysis on the almost automorphic solutions for impulsive neural networks with impulsive effect
In order to make up for the deficiency, we think that it is of importance to discuss pseudo almost automorphic solutions of quaternion-valued cellular neural networks with delays

Summary

INTRODUCTION

As is known to us, the dynamical property of cellular neural networks has attracted great attention of scholars from all over the world since cellular neural networks can be successfully applied to various areas such as image processing, associative memories, artificial intelligence, disease diagnosis and so on [1]–[16]. C. Xu: On Pseudo Almost Automorphic Solutions to Quaternion-Valued Cellular Neural Networks With Delays much attention from many researchers. Some excellent works on pseudo almost automorphic solutions on neural networks have been displayed. Zhu et al [39] studied the existence and exponential stability of pseudo almost automorphic solutions to delayed Cohen-Grossberg neural networks. It is a pity that very few authors have investigated the pseudo almost automorphic solutions of quaternion-valued cellular neural networks with delays. In order to make up for the deficiency, we think that it is of importance to discuss pseudo almost automorphic solutions of quaternion-valued cellular neural networks with delays. Stimulated by the above viewpoint, in this manuscript, we consider the dynamics of the following quaternion-valued cellular neural networks with delays:.

PRELIMINARIES

COMPUTER SIMULATIONS

CONCLUSION