| 带可变的分布式延时的高阶Cohen-Grossberg神经网络的动力学行为分析(英文) |
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| 引用本文： | 刘艳.带可变的分布式延时的高阶Cohen-Grossberg神经网络的动力学行为分析(英文)[J].复旦学报(自然科学版),2011(1). |
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| 作者姓名： | 刘艳 |
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| 作者单位： | 复旦大学数学科学学院; |
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| 摘 要： | 对于高阶和低阶CGNN的工作前人做了很多,其中论及的网络都属于文章中讨论的高阶Cohen-Grossberg神经网络的某种特殊情况.讨论了此类网络平衡点的存在性和稳定性.引理2给出了系统(3)何时有平衡点的一个判断,定理1和定理2则讨论了不同条件下引理中平衡点的稳定性.每一个引理和定理都有简单的式子便于计算和判断.研究的带有可变的分布式延时的Cohen-Grossberg神经网络的平衡点的存在性和稳定性的结果具有普遍的意义,可以用于一大类CGNN的平衡点存在性和稳定性的判定上.
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| 关 键 词： | 高阶神经网络 Cohen-Grossberg 可变的分布式延迟 平衡点的存在性和稳定性 指数稳定 |
Dynamics of Higher-order Cohen-Grossberg Neural Networks with Variable and Distributed Delays |
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| LIU Yan.Dynamics of Higher-order Cohen-Grossberg Neural Networks with Variable and Distributed Delays[J].Journal of Fudan University(Natural Science),2011(1). |
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| Authors: | LIU Yan |
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| Institution: | LIU Yan(School of Mathematical Sciences,Fudan University,Shanghai 200433,China) |
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| Abstract: | Many works have been done on higher-order and lower-oder Hopfield neural networks(e.g.CGNN),which is one special class of higher-order CGNN.The existence and stability of equilibrium in CGNN system are discussed.Lemma 2 tell us when there exists an equilibrium for system(3).Theorem 1 and Theorem 2 discuss about the stability of equilibrium.All the lemma and theorems have simple form.With variable and distributed delays,the result of the model can be used in a large class of CGNN. |
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| Keywords: | higher-order neural network Cohen-Grossberg variable and distributed delays existence and stability of equilibrium exponential stability |
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