Stability and Hopf bifurcation analysis of fractional-order complex-valued neural networks with time delays

R Rakkiyappan,Jinde Cao,K Udhayakumar,G Velmurugan,Ahmed Alsaedi

doi:10.1186/s13662-017-1266-3

Abstract

This paper considers a class of fractional-order complex-valued Hopfield neural networks (CVHNNs) with time delay for analyzing the dynamic behaviors such as local asymptotic stability and Hopf bifurcation. In the case of a neural network with hub and ring structure, the stability of the equilibrium state is investigated by analyzing the eigenvalue of the corresponding characteristic matrix for the hub and ring structured fractional-order time delay models using a Laplace transformation for the Caputo-fractional derivatives. Some sufficient conditions are established to guarantee the uniqueness of the equilibrium point. In addition, conditions for the occurrence of a Hopf bifurcation are also presented. Finally, numerical examples are given to demonstrate the effectiveness of the derived results.

Highlights

The discipline of neural networks, as other fields of science, has a long history of evolution with lots of ups and downs
Motivated by the above discussion, in this paper we investigate the stability and Hopf bifurcation of the fractional-order complex-valued Hopfield neural networks (CVHNNs) with time delays in two types of structures named ring and hub structures
The class of fractional-order CVHNNs with hub and ring structured system is considered in a time delay sense

Summary

Introduction

The discipline of neural networks, as other fields of science, has a long history of evolution with lots of ups and downs. In the last few decades, the subjective analysis of neural networks (NNs) has received huge attention because of its strong applications in numerous fields such as signal and image processing, associative memories, combinatorial optimization and many others [ – ]. Such practical applications of NNs are strongly dependent on the qualitative behaviors of NNs. such practical applications of NNs are strongly dependent on the qualitative behaviors of NNs In both biological and physical models, the occurrence of time delays plays an important role. The problem of fixed-time synchronization of memristive neural networks was studied in [ ]

Objectives

Conclusion