三元环状神经网络的稳定性

数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1654-1665.

三元环状神经网络的稳定性

邹劭芬^1,2|王耀南²|黄立宏¹

1.湖南大学数学与计量经济学院长沙 410082|2.湖南大学电气与信息工程学院长沙 |410082

收稿日期:2008-10-22 修回日期:2009-10-29 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
湖南省博士后基金(2009RS3004)、国家自然科学基金(60775047, 10771055, 60835004)及国家863项目(2007AA04Z244)资助

Stability of a Ring Neural Network with Delays

ZOU Shao-Fen^1,2, WANG Yao-Na², HUANG Li-Hong¹

1.College of Mathematics and Econometrics, Hunan University, Changsha 410082;
2.College of Electrical and Information Engineering, Hunan University, Changsha 410082

Received:2008-10-22 Revised:2009-10-29 Online:2010-12-25 Published:2010-12-25
Supported by:
湖南省博士后基金(2009RS3004)、国家自然科学基金(60775047, 10771055, 60835004)及国家863项目(2007AA04Z244)资助

摘要/Abstract

摘要：

该文针对一个带自反馈的多时滞环状神经网络系统, 在整个参数空间中, 分区域系统完整地讨论了系统平凡解稳定与不稳定的条件, 并根据正实部特征根个数依参数变动的变化规律, 给出了不同参数条件下平凡解的相应最大稳定区域边界, 改进和完善了先前的结果.

关键词: 神经网络, 时滞, 线性稳定性, 最大稳定区域

Abstract:

A system of ring neural network with self-feedback and multiple delays is considered. Conditions for the stability and unstability of the trivial solution of this system are completely represented in a parameter space. According to the
regulation of the variation of the number of eigenvalues with positive real parts, for different parameters, the authors investigate the boundary of the largest stability set, improve and complete the former conclusions

Key words: Neural network, Delay, Linear stability, Largest stability set

中图分类号:

34K20

邹劭芬, 王耀南, 黄立宏. 三元环状神经网络的稳定性[J]. 数学物理学报, 2010, 30(6): 1654-1665.

ZOU Shao-Fen, WANG Yao-Na, HUANG Li-Hong. Stability of a Ring Neural Network with Delays[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1654-1665.

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