| THE STABILITY OF A KIND OF DISCRETE-TIME HOPFIELD NEURAL NETWORKS WITH ASYMPTOTICAL WEIGHTED MATRICES |
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| 引用本文： | Guo Shujuan Ruan Jiong Tu Qingwei (Dept. of Informal Science,Jiangsu Polytechnic University,Changzhou 213164, Dept. of Math.,Fudan University,Shanghai 200433). THE STABILITY OF A KIND OF DISCRETE-TIME HOPFIELD NEURAL NETWORKS WITH ASYMPTOTICAL WEIGHTED MATRICES[J]. Annals of Differential Equations, 2006, 22(4): 489-495 |
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| 作者姓名： | Guo Shujuan Ruan Jiong Tu Qingwei (Dept. of Informal Science Jiangsu Polytechnic University Changzhou 213164 Dept. of Math. Fudan University Shanghai 200433) |
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| 作者单位： | Dept. of Informal Science，Jiangsu Polytechnic University，Changzhou 213164; Dept. of Math.，Fudan University，Shanghai 200433 |
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| 摘 要： | In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale's invariance principle in difference equation is applied.
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| 关 键 词： | 神经网络 Lassale恒定原理 不对称权重矩阵 平衡性 |
THE STABILITY OF A KIND OF DISCRETE-TIME HOPFIELD NEURAL NETWORKS WITH ASYMPTOTICAL WEIGHTED MATRICES |
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| Guo Shujuan Ruan Jiong Tu Qingwei. THE STABILITY OF A KIND OF DISCRETE-TIME HOPFIELD NEURAL NETWORKS WITH ASYMPTOTICAL WEIGHTED MATRICES[J]. 微分方程年刊(英文版), 2006, 22(4): 489-495 |
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| Authors: | Guo Shujuan Ruan Jiong Tu Qingwei |
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| Affiliation: | [1]Dept. of Informal Science, Jiangsu Polytechnic University, Changzhou 213164 [2]Dept. of Math., Fudan University, Shanghai 200433 |
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| Abstract: | In this paper, the authors analyze the stability of a kind of discrete-time Hopfield neural network with asymptotical weighted matrix, which can be expressed as the product of a positive definite diagonal matrix and a symmetric matrix. We obtain that it has asymptotically stable equilibriums if the network is updated asynchronously, and asymptotically stable equilibriums or vibrating final stage with 2 period if updated synchronously. To prove these, Lassale's invariance principle in difference equation is applied. |
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| Keywords: | Hopfield neural network Lassale's invariance principle asymmetric weighted matrix equilibriums asymptotic stable vibration |
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