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Hopf Bifurcation on a Two-Neuron System with Distributed Delays: A Frequency Domain Approach

Hopf Bifurcation on a Two-Neuron System with Distributed Delays: A Frequency Domain Approach In this paper, a more general two-neuron model with distributed delays and weak kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. Furthermore, we found that if the mean delay is used as a bifurcation parameter, Hopf bifurcation occurs for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determine by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Hopf Bifurcation on a Two-Neuron System with Distributed Delays: A Frequency Domain Approach

Liao, Xiaofeng; Li, Shaowen; Wong, Kwok-wo
Nonlinear Dynamics , Volume 31 (3) – Oct 7, 2004
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28 pages

 
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References (53)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
DOI
10.1023/A:1022928118143
Publisher site
See Article on Publisher Site

Abstract

In this paper, a more general two-neuron model with distributed delays and weak kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. Furthermore, we found that if the mean delay is used as a bifurcation parameter, Hopf bifurcation occurs for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determine by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given.

Journal

Nonlinear Dynamics – Springer Journals

Published: Oct 7, 2004

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