时滞回归神经反馈系统的稳定性及Hopf分支  

Stability and Hopf Bifurcation for Recurrent Neural Feedback Systems with Delay

作　　者：马文联[1] 孙艳[1] 魏俊杰[2] 崔凯[2] 

机构地区：[1]长春光学精密机械学院数学系,长春130022 [2]东北师范大学数学系,长春130024

出　　处：《吉林大学自然科学学报》1999年第2期23-27,共5页Acta Scientiarum Naturalium Universitatis Jilinensis

摘　　要：研究时滞回归神经反馈系统， 给出该系统的稳定性及 Ｈｏｐｆ 分支存在的条件． 利用“规范型”的方法获得 Ｈｏｐｆ 分支方向和分支周期解的稳定性的计算公式．The present paper deals with the Hopf bifurcation for recurrent neural feedback systems with delay. According to the conclusions, drawn by the method of Cooke and Grossman, on the distribution of the roots of transcendental equation and with the delay as a parameter. We have found the existence of the stability switch of this system and presented some conditions that garantee the stability and the existence of Hopf Bifurcation. And we used the methods of “Normal Form” to obtain some formulas about deciding the direction of Hopf bifurcation and the stability of bifurcation periodic roots.

关 键 词：时滞 HOPF分支 稳定性 神经反馈系统 数学模型 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O175.13[自动化与计算机技术—控制科学与工程]