Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays

被引：86
|
作者：
Wang, Zhen [1 ,2 ]
Li, Li [1 ]
Li, Yuxia [2 ]
Cheng, Zunshui [3 ]
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] Qingdao Univ Sci & Technol, Coll Math & Phys, Qingdao 266061, Peoples R China
来源：
NEURAL PROCESSING LETTERS | 2018年 / 48卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Three-neuron network; Distributed delay; Discrete delay; Stability; Hopf bifurcation; Periodic solution; GROSSBERG NEURAL-NETWORKS; 2-NEURON NETWORK; EXPONENTIAL STABILITY; SYSTEM; SYNCHRONIZATION; DYNAMICS; CHAOS; MODEL;
D O I：
10.1007/s11063-017-9754-8
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, a class of three-neuron network with discrete and distributed delays is introduced. We first give a detailed Hopf bifurcation analysis for the proposed network. Choosing the discrete time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Moreover, by using the normal form theory and center manifold theorem, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are derived. Finally, numerical simulations are presented to demonstrate the effectiveness of our theoretical results.
引用
收藏
页码：1481 / 1502
页数：22
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