| 一类具时滞的神经网络模型的Hopf分支 |
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| 引用本文： | 段文英,魏俊杰,沈启宏.一类具时滞的神经网络模型的Hopf分支[J].数学年刊A辑(中文版),2003(6). |
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| 作者姓名： | 段文英 魏俊杰 沈启宏 |
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| 作者单位： | 东北林业大学数学系 哈尔滨150040
(段文英)，哈尔滨工业大学数学系 哈尔滨150001
(魏俊杰)，东北师范大学数学系 长春130024(沈启宏) |
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| 基金项目： | 国家自然科学基金(No.19831030)，黑龙江省自然科学基金(No.20030205)资助的项目 |
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| 摘 要： | 本文研究了一类由两个神经元构成的具时滞的神经网络模型的动力学性质,即利用指数多项式的D-划分法讨论了平衡点的稳定性和局部Hopf分支的存在性,然后利用规范型和中心流形理论给出了分支性质的计算公式,又用度理论研究了周期解的全局存在性.
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| 关 键 词： | 时滞 神经网络 分支 |
HOPF BIFURCATION OF A NEURAL NETWORK MODEL WITH TIME DELAY |
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| DUAN Wenying WEI Junjie SHEN Qihong.HOPF BIFURCATION OF A NEURAL NETWORK MODEL WITH TIME DELAY[J].Chinese Annals of Mathematics,2003(6). |
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| Authors: | DUAN Wenying WEI Junjie SHEN Qihong |
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| Institution: | DUAN Wenying WEI Junjie SHEN Qihong
Department of Mathematics,Northeast Forestry University,Harbin 150040,China.
E-mail: wenying@0451.com Department of Mathematics,Harbin Techology University,Harbin 150001,China.
E-mail: weijj@hit.edu.cn
Department of Mathematics,Northeast Normal University,Changchun 130024,China. |
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| Abstract: | This paper investigates the property of dynamics property of a neural network model with thime delay formed by two neurons. That is, the authors discuss the stability of the equilibrium point and the existence of the local Hopf bifurcation by the D-division method of the exponential polynomial. Also the authors exhibit calculating formulas about the property of bifurcation with the normal form and the center manifold theory, and study the global existence of the periodic solutions by degree theory. |
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| Keywords: | Neural network Time delay Bifurcation |
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