Complete stability of delayed recurrent neural networks with Gaussian activation functions

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• 作者：Peng Liu^a ; ^b ; ^{liupengjz@163.com} ; Zhigang Zeng^a ; ^b ; ^{zgzeng@hust.edu.cn} ; Jun Wang^c ; ^{jwang.cs@cityu.edu.hk}
• 关键词：Recurrent neural networks ; Complete stability ; Time-varying delays ; Gaussian functions
• 刊名：Neural Networks
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：85
• 期：Complete
• 页码：21-32
• 全文大小：795 K
• 卷排序：85

文摘

This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular MM-matrix, some sufficient conditions are obtained to ensure that for an nn-neuron neural network, there are exactly 3k3k equilibrium points with 0≤k≤n0≤k≤n, among which 2k2k and 3k−2k3k−2k equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results.