Bifurcation Analysis in a Three-Neuron Artificial Neural Network Model with Distributed Delays

被引：0
|
作者：
Changjin Xu
Qiming Zhang
Yusen Wu
机构：
[1] Guizhou University of Finance and Economics,Guizhou Key Laboratory of Economics System Simulation
[2] Hunan University of Technology,College of Science
[3] Henan University of Science and Technology,School of Mathematics and Statistics
来源：
Neural Processing Letters | 2016年 / 44卷
关键词：
Artificial neural network; Stability; Hopf bifurcation; Distributed delay; Periodic solution; 34K20; 34C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a three-neuron artificial neural network model with distributed delays is considered. Its dynamics is investigated in term of the linear stability analysis and Hopf bifurcation analysis. By regarding the sum of two delays as a bifurcation parameter and analyzing the associated characteristic equation, we find that Hopf bifurcation occurs when the bifurcation parameter passes through some certain values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using the normal form method and center manifold theory. Finally, computer simulations are given to support the theoretical predictions.
引用
收藏
页码：343 / 373
页数：30
相关论文
共 50 条
  • [1] Bifurcation Analysis in a Three-Neuron Artificial Neural Network Model with Distributed Delays
    Xu, Changjin
    Zhang, Qiming
    Wu, Yusen
    NEURAL PROCESSING LETTERS, 2016, 44 (02) : 343 - 373
  • [2] Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays
    Wang, Zhen
    Li, Li
    Li, Yuxia
    Cheng, Zunshui
    NEURAL PROCESSING LETTERS, 2018, 48 (03) : 1481 - 1502
  • [3] Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays
    Zhen Wang
    Li Li
    Yuxia Li
    Zunshui Cheng
    Neural Processing Letters, 2018, 48 : 1481 - 1502
  • [4] Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays
    Han, Yanyan
    Song, Yongli
    NONLINEAR DYNAMICS, 2012, 69 (1-2) : 357 - 370
  • [5] Stability and Hopf bifurcation in a three-neuron unidirectional ring with distributed delays
    Yanyan Han
    Yongli Song
    Nonlinear Dynamics, 2012, 69 : 357 - 370
  • [6] Bifurcation analysis on a generalized recurrent neural network with two interconnected three-neuron components
    Hajihosseini, Amirhossein
    Maleki, Farzaneh
    Lamooki, Gholam Reza Rokni
    CHAOS SOLITONS & FRACTALS, 2011, 44 (11) : 1004 - 1019
  • [7] Stability and Hopf bifurcation analysis of a pair of three-neuron loops with time delays
    Xiaochen Mao
    Nonlinear Dynamics, 2012, 68 : 151 - 159
  • [8] Periodic oscillation for a three-neuron network with delays
    Zhang, ZQ
    Guo, SJ
    APPLIED MATHEMATICS LETTERS, 2003, 16 (08) : 1251 - 1255
  • [9] Stability and Hopf bifurcation analysis of a pair of three-neuron loops with time delays
    Mao, Xiaochen
    NONLINEAR DYNAMICS, 2012, 68 (1-2) : 151 - 159
  • [10] Bifurcation and stability analysis of a neural network model with distributed delays
    Cheng, Zunshui
    Cao, Jinde
    NONLINEAR DYNAMICS, 2006, 46 (04) : 363 - 373
12345