Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

被引：185

作者：

Li, Li ^{[1
]}

Wang, Zhen ^{[1
,2
]}

Li, Yuxia ^{[2
]}

Shen, Hao ^{[3
]}

Lu, Junwei ^{[4
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Peoples R China

[3] Anhui Univ Technol, Sch Elect Engn & Informat, Maanshan 243002, Peoples R China

[4] Nanjing Normal Univ, Sch Elect & Automat Engn, Nanjing 210023, Jiangsu, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 330卷

基金：

中国国家自然科学基金;

关键词：

Hopf bifurcation; Complex-valued; Neural network; Discrete delays; Distributed delays; EXPONENTIAL STABILITY; DYNAMICAL NETWORKS; 2-NEURON SYSTEM; SAMPLED-DATA; SYNCHRONIZATION; MEMORY;

D O I：

10.1016/j.amc.2018.02.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a class of complex-valued neural network model with discrete and distributed delays is proposed. Regarding the discrete time delay as the bifurcating parameter, the problem of Hopf bifurcation in the newly-proposed complex-valued neural network model is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the normal form theory and center manifold theorem, some sufficient conditions which determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Finally, a numerical example is given to illustrate the validity of the theoretical results. (c) 2018 Elsevier Inc. All rights reserved.

引用

页码：152 / 169

页数：18

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