| 具有反应扩散的神经网络的稳定性分析 |
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| 引用本文： | 郑伟范,张继业.具有反应扩散的神经网络的稳定性分析[J].西南交通大学学报,2004,39(1):117-120. |
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| 作者姓名： | 郑伟范 张继业 |
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| 作者单位： | 1. 西南交通大学计算机与通信工程学院,四川,成都,610031
2. 西南交通大学牵引动力国家实验室,四川,成都,610031 |
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| 基金项目： | 国家自然科学基金资助项目(10272091) |
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| 摘 要： | 通过构造适当的平均Luapunov函数，利用M矩阵理论，研究了一类具有反应扩散的Hopfield神经网络的全局稳定性．在放松神经网络的激活函数的有界性、单调递增性和可微性的条件下，得到了神经网络的全局渐近稳定的条件．这些条件适合于神经网络的关联矩阵为对称或非对称矩阵、激活函数为非单调的情况．
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| 关 键 词： | 神经网络 反应扩散 全局渐近稳定 M矩阵 Luapunov函数 |
| 文章编号： | 0258-2724(2004)01-0117-04 |
Globally Asymptotic Stability of Neural Networks with Reaction-Diffusion |
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| ZHENG Wei-fan,ZHANG Ji-ye.Globally Asymptotic Stability of Neural Networks with Reaction-Diffusion[J].Journal of Southwest Jiaotong University,2004,39(1):117-120. |
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| Authors: | ZHENG Wei-fan ZHANG Ji-ye |
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| Institution: | ZHENG Wei-fan~1,ZHANG Ji-ye~2 |
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| Abstract: | Even type Lyapunov functions were constructed based on M-matrix theory to study the globally asymptotic stability of Hopfield networks with reaction-diffusion. These networks are generalized without assuming the boundedness, monotonicity and differenciability of the activate functions. The conditions were obtained for globally asymptotic stability of the generalized Hopfield networks, where the interconnection matrices are symmetric or non-asymmetric and the neural activate functions are non-monotonic. |
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| Keywords: | neural networks reaction-diffusion global asymptotic stability M-matrix Lyapunov function |
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