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 103 条
  • [1] Kaslik E(2011)Multiple periodic solutions in impulsive hybird neural networks with delays Appl Math Comput 217 4890-4899
  • [2] Sivasundaram S(2010)Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with distributed delays Commun Nonlinear Sci Numer Simul 15 189-204
  • [3] Wang BX(2004)Stability and synchronization of a ring of identical cells with delayed coupling J Dyn Differ Equ 16 709-744
  • [4] Jian JG(2005)Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling Nonlinearity 18 2827-2846
  • [5] Yuan Y(2008)Two parameter bifurcations in a network of two neurons with multiple delays J Differ Equ 244 444-486
  • [6] Campbell SA(2004)Bifurcation analysis and existence of periodic solutions in a simple neural network delays Chaos 14 940-953
  • [7] Campbell SA(1998)Symmetric functional differential equations and neural networks with memory Trans Am Math Soc 350 4799-4838
  • [8] Yuan Y(2006)Multiple bifurcation analysis in a neural network model with delays Int J Bifurc Chaos 16 2903-2913
  • [9] Bungay SD(2012)Spatio-temporal patterns of Hopf bifurcating periodic oscillations in a pair of identical tri-neuron network loops Commun Nonlinear Sci Numer Simul 17 943-952
  • [10] Guo SJ(2013)Frequency domain approach to computational analysis of bifurcation and periodic solution in a two-neuron network model with distributed delays and self-feedbacks Neurocomputing 99 206-213
12345678910