Existence and Global Attractivity of Pseudo Almost Periodic Solutions for Clifford-Valued Fuzzy Neural Networks with Proportional Delays

Wen Lv,Bing Li

doi:10.3390/math9243306

Abstract

In this paper, Clifford-valued fuzzy neural networks with proportional delays, whose leakage term coefficients are also Clifford numbers, are considered. Based on the Banach fixed point theorem and differential inequality technique, we use a direct method to obtain the existence, uniqueness, and global attractivity of pseudo almost periodic solutions for the considered networks. Finally, we provide a numerical example to illustrate the feasibility of our results. Our results are new.

Highlights

The Clifford-valued neural network is a generalization of a real-valued neural network, complex-valued neural network, and quaternion-valued neural network, and has been shown superior to a real-valued neural network [1,2]
Many existing results are obtained by decomposing a Clifford-valued system into a real-value system [3,4,5,6]. It is a meaningful and challenging work to study the dynamics of Clifford-valued systems via a direct method; that is, without decomposing Clifford-valued systems into real-valued systems [7,8,9,10,11]
Many scholars have studied the dynamics of neural networks with proportional delays

Summary

Introduction

The Clifford-valued neural network is a generalization of a real-valued neural network, complex-valued neural network, and quaternion-valued neural network, and has been shown superior to a real-valued neural network [1,2]. The existence and global exponential stability of (μ, ν)-pseudo almost periodic solutions to a class of Clifford-valued higher order Hopfield neural networks, with bounded multiple discrete delays whose leakage term coefficients are . Up until now, the results of almost periodic oscillation of neural networks with proportional delays and whose leakage term coefficient s are Clifford numbers, have not been reported. Inspired by the above analysis, the purpose of this paper is to study the existence and attraction of pseudo almost periodic solutions for a class of Clifford-valued fuzzy neural networks with proportional delays and whose leakage term coefficients are Clifford numbers. To the best of our knowledge, this is the first paper to study the existence and attractivity of pseudo almost periodic solutions of Clifford-valued neural networks with proportional delay and whose leakage coefficients are Clifford numbers.

Model Description and Preliminaries

Pseudo Almost Periodic Solutions

Global Attractivity

An Example

Conclusions