| 二阶Hopfield神经网络周期解的存在性 |
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| 引用本文： | 王培光,廉海容.二阶Hopfield神经网络周期解的存在性[J].应用数学学报,2006,29(1):104-110. |
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| 作者姓名： | 王培光 廉海容 |
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| 作者单位： | 1. 河北大学电子信息工程学院,保定,071002
2. 北京理工大学应用数学系,北京,100081 |
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| 基金项目： | 教育部留学基金;河北省自然科学基金 |
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| 摘 要： | 本文讨论了一类带有时滞的二阶Hopfield神经网络周期解的存在性问题。首先利用Brouwer不动点定理证明了平衡点的存在性,通过平衡点和拉格朗日中值定理,将高阶神经网络模型转换为一阶模型,然后利用重合度理论给出了周期解存在的充分条件。
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| 关 键 词： | 二阶Hopfield神经网络 时滞 周期解 重合度理论 |
| 收稿时间： | 2003-11-24 |
| 修稿时间： | 2003-11-24 |
Existence of Periodic Solutions for Second-order Hopfield Neural Network |
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| WANG PEIGUANG,LIAN HAIRONG.Existence of Periodic Solutions for Second-order Hopfield Neural Network[J].Acta Mathematicae Applicatae Sinica,2006,29(1):104-110. |
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| Authors: | WANG PEIGUANG LIAN HAIRONG |
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| Institution: | 1,College of Electronic Information and Engineering, Hebei University, Baoding 071002;2,Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081 |
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| Abstract: | This paper deals with the existence of periodic solutions for second order Hopfield neural network with time delays. The existence of equilibrium of such neural network is obtained by using Brouwer's fixed-point theorem. While through the equilibrim and the mean value of Lagrange theorem, the neural network is changed into a lower-order one. Then sufficient conditions are established for the existence of periodic solutions. |
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| Keywords: | second-order Hopfield neural network delay periodic solution coincidence degree |
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