| 具有扩散影响的Hopfield型神经网络的全局渐近稳定性 |
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| 引用本文： | 颜向平,李万同.具有扩散影响的Hopfield型神经网络的全局渐近稳定性[J].应用数学和力学,2007,28(3):328-334. |
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| 作者姓名： | 颜向平 李万同 |
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| 作者单位： | 1. 兰州交通大学,数学系,兰州,730070
2. 兰州大学,数学与统计学院,兰州,730000 |
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| 基金项目： | 国家自然科学基金;甘肃省自然科学基金 |
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| 摘 要： | 对具有扩散影响的Hopfield型神经网络平衡点的存在唯一性和全局渐近稳定性进行了研究.在激活函数单调非减、可微且关联矩阵和Liapunov对角稳定矩阵有关时,利用拓扑度理论得到了系统平衡点存在的充分条件.通过构造适当的平均Liapunov函数,分析了系统平衡点的全局渐近稳定性.所得结论表明系统的平衡点(如果存在)是全局渐近稳定的而且也蕴含着系统的平衡点的唯一性.
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| 关 键 词： | 扩散 Hopfield型神经网络 平衡点 全局渐近稳定性 |
| 文章编号： | 1000-0887（2007）03-0328-07 |
| 修稿时间： | 2006-09-18 |
Global Asymptotic Stability for Hopfield-Type Neural Networks With Diffusion Effects |
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| YAN Xiang-ping,LI Wan-tong.Global Asymptotic Stability for Hopfield-Type Neural Networks With Diffusion Effects[J].Applied Mathematics and Mechanics,2007,28(3):328-334. |
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| Authors: | YAN Xiang-ping LI Wan-tong |
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| Institution: | 1. Department ofMathematics,Lanzhou Jiaotong University,Lanzhou 73070, P. R. China; 2. School of Mathematics and Statistics, Lanzhou University |
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| Abstract: | The existence,uniqueness and global asymptotic stability of the equilibrium for Hopfield-type neural networks with diffusion were discussed.The sufficient conditions of the existence and uniqueness of the equilibrium of the system were obtained by applying the topological degree theory when the activation functions are monotonous non-decreasing and differential,and the interconnected matrix is related to the Lianupov diagonal stable matrix.By constructing the average Liapunov functions,the global asymptotic stability of the equilibrium of the system was obtained. |
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| Keywords: | diffusion neural networks equilibrium global asymptotic stability |
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