具时滞的二维神经网络模型的分支  

Bifurcation in a Two-Dimensional Neural Network Model With Delay

作　　者：魏俊杰[1] 张春蕊[2] 李秀玲[3] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001 [2]东北林业大学森林植物生态学教育部重点实验室,哈尔滨150040 [3]长春税务学院基础部,长春130022

出　　处：《应用数学和力学》2005年第2期193-200,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(19831030)

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。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.

关 键 词：神经网络 中心流形 pitchfork分支 HOPF分支 

分 类 号：O175.5[理学—数学]