Stability and Bifurcation Analysis of a Network of Four Neurons With Time Delays-Reference-Cited by-同舟云学术

Stability and Bifurcation Analysis of a Network of Four Neurons With Time Delays

Published:2010-06-29 Issue:4 Volume:5 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Mao Xiaochen¹,Hu Haiyan²

Affiliation:

1. MOE Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China; Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, 210098 Nanjing, China

2. MOE Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China

Abstract

This paper reveals the dynamical behaviors of a bidirectional neural network consisting of four neurons with delayed nearest-neighbor and shortcut connections. The criterion of the global asymptotic stability of the trivial equilibrium of the network is derived by means of a suitable Lyapunov functional. The local stability of the trivial equilibrium is investigated by analyzing the distributions of roots of the associated characteristic equation. The sufficient conditions for the existence of nontrivial synchronous and asynchronous equilibria and periodic oscillations arising from codimension one bifurcations are obtained. Multistability near the codimension two bifurcation points is presented. Numerical simulations are given to validate the theoretical analysis.

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4000317/5510436/041001_1.pdf

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