时延细胞神经网络的全局渐近稳定性

J4 ›› 2013, Vol. 35 ›› Issue (7): 82-86.

时延细胞神经网络的全局渐近稳定性

刘小群

(华南理工大学经济与贸易学院,广东广州 510006)

收稿日期:2012-03-21 修回日期:2012-08-27 出版日期:2013-07-25 发布日期:2013-07-25

Asymptotic stability of delayed cellular neural networks

LIU Xiaoqun

(School of Economics and Commerce,South China University of Technology,Guangzhou 510006,China)

Received:2012-03-21 Revised:2012-08-27 Online:2013-07-25 Published:2013-07-25

摘要/Abstract

摘要：

通过构造新的Lyapunov泛函，在Lyapunov泛函中巧妙引入可调的实参数，并结合不等式运用的一些技巧，讨论了时延细胞神经网络的全局渐近稳定性问题，得到了该模型的平衡点全局渐近稳定的一些新的充分条件。所得的结果改进推广了已有文献中相应的一些结论，并且可应用于以前所不能处理的若干情形。理论分析和数学推导表明，全局渐近稳定性的一个简单充分判据与时延是有关的。所得结果突出了时延对于细胞神经网络的全局渐近稳定性的影响，这对于设计带时延的细胞神经网络有着重要的参考价值。此外，通过实例说明了相应结果的应用，这在理论上和应用中都有着重要的意义。

关键词: 时延细胞神经网络, 全局渐近稳定性, Lyapunov泛函

Abstract:

By constructing the new Lyapunov functional, ingeniously importing real parameters which can be adjusted, and making use of the inequalities, the global asymptotic stability of delayed cellular neural networks with variable coefficient was discussed and new sufficient conditions were obtained. The results of this paper improve, extend, unify and complement a number of existing results. They also handle a number of cases not covered by known criteria. Theoretical analysis and mathematical derivation show that the global asymptotic stability is related to the delay. The results we obtained highlight the impact of delay on the global asymptotic stability of cellular neural networks. This is of important guiding significance for the design of cellular neural networks with delay. Interesting examples were included to show the versatility of our results. And they greatly enlarge the area of designing neural networks. This has important significance in both theory and application.

Key words: delayed cellular neural networks;global asymptotic stability;Lyapunov functional

刘小群. 时延细胞神经网络的全局渐近稳定性[J]. J4, 2013, 35(7): 82-86.

LIU Xiaoqun. Asymptotic stability of delayed cellular neural networks [J]. J4, 2013, 35(7): 82-86.