Bifurcation in a Two-Dimensional Neural Network Model With Delay

WEI Jun-jie; ZHANG Chun-rui; LI Xiu-ling

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(2): 193-200

WEI Jun-jie, ZHANG Chun-rui, LI Xiu-ling. Bifurcation in a Two-Dimensional Neural Network Model With Delay[J]. Applied Mathematics and Mechanics, 2005, 26(2): 193-200.

Citation:

WEI Jun-jie, ZHANG Chun-rui, LI Xiu-ling. Bifurcation in a Two-Dimensional Neural Network Model With Delay[J]. Applied Mathematics and Mechanics, 2005, 26(2): 193-200.

Citation:

WEI Jun-jie, ZHANG Chun-rui, LI Xiu-ling. Bifurcation in a Two-Dimensional Neural Network Model With Delay[J]. Applied Mathematics and Mechanics, 2005, 26(2): 193-200.

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Bifurcation in a Two-Dimensional Neural Network Model With Delay

1.
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China;

Received Date: 2003-05-20
Rev Recd Date: 2004-09-24
Publish Date: 2005-02-15

Abstract

Abstract

A kind of 2-dimensional neural network model with delay is considered.By analyzing the distribution of the roots of the characteristic equation associated with the model,a bifurcation diagram was drawn in an appropriate parameter plane.It is found that a line is a pitchfork bifurcation curve.Further more,the stability of each fixed point and existence of Hopf bifurcation were obtained.Finally,the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.
- neural network,
- centre manifold,
- pitchfork bifurcation,
- Hopf bifurcation

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References(8)

References

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