具时滞的二维神经网络模型的分支

基金项目: 国家自然科学基金资助项目(19831030)

Bifurcation in a Two-Dimensional Neural Network Model With Delay

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

摘要: 研究了一类具时滞的二维神经网络模型．通过对该模型的特征方程根的分布分析, 在适当的参数平面上给出了分支图．得到了pitchfork分支曲线是一条直线,进而研究了每个平衡点的稳定性和Hopf分支的存在性．最后,利用规范性方法和中心流形理论,得到了Hopf分支的分支方向和分支周期界的稳定性．
- 神经网络 /
- 中心流形 /
- pitchfork分支 /
- Hopf分支
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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