Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach

Huamin Wang,Shiping Wen,Jie Tan

doi:10.1109/access.2020.2994554

Abstract

With the application of quaternion in technology, quaternion-valued neural networks (QVNNs) have attracted many scholars' attention in recent years. For the existing results, dynamical behavior is an important studying side. In this paper, we mainly research the existence, uniqueness and exponential stability criteria of solutions for the QVNNs with discrete time-varying delays and distributed delays by means of generalized 2-norm. In order to avoid the noncommutativity of quaternion multiplication, the QVDNN system is firstly decomposed into four real-number systems by Hamilton rules. Then, we obtain the sufficient criteria for the existence, uniqueness and exponential stability of solutions by special Lyapunov-type functional, Cauchy convergence principle and monotone function. Furthermore, several corollaries are derived from the main results. Finally, we give one numerical example and its simulated figures to illustrate the effectiveness of the obtained conclusion.

Highlights

After the models of various neural networks (NNs) (Hopfield NNs, Cohen-Grossberg NNs, memristive NNs, etc.) were built [1]–[3], they have been widely used to research pattern recognition, optimization problems, intelligent control, and so on
Based on the above analyses, this paper focuses on the existence and exponential stability of solutions for the quaternion-valued neural networks (QVNNs) with discrete time-varying delays and distributed delays by generalized 2-norm ({ξ, 2}-norm)
This paper has focused on the existence and exponential stability of solutions of the QVNNs with discrete time-varying delays and distributed delays by means of {ξ, 2}-norm

Summary

INTRODUCTION

After the models of various neural networks (NNs) (Hopfield NNs, Cohen-Grossberg NNs, memristive NNs, etc.) were built [1]–[3], they have been widely used to research pattern recognition, optimization problems, intelligent control, and so on. In [13], [15], [16], some important stability conclusions were obtained for those NNs with discrete and distributed delays. The method of ∞-norm can not be used to study some dynamical behaviors by 1-norm or 2-norm, the similar results can be derived by generalized 1-norm if some results of QVDNNs can be obtained by generalized 2-norm It is worthy studying the stability of QVNNs with discrete time-varying delays and distributed delays by {ξ, 2}-norm, which remains an open problem. By constructing {ξ, 2}-norm-type Lyapunov functional, the existence, uniqueness and exponential stability sufficient criteria of the discrete-distributed-delayed QVNNs are obtained by Cauchy convergence principle and monotone function. One numerical example about QVNNs with discrete time-varying delays and distributed delays is given to illustrate the effectiveness of the obtained conclusions.

PRELIMINARIES

MAIN RESULTS

NUMERICAL EXAMPLE

CONCLUSIONS