Stability and attractive basins of multiple equilibria in delayed two-neuron networks

Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation flmctions of 2r （r 〉 1） corner points is studied. Sufficient conditions are established for checking the existence of （2r ＋ 1）2 equilibria in delayed recurrent neural networks. Under these condi...

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Published inChinese physics B Vol. 21; no. 7; pp. 216 - 223
Main Author 黄玉娇 张化光 王占山
Format Journal Article
LanguageEnglish
Published 01.07.2012
Subjects
Activation
Activation analysis
Basins
Corners
Invariants
Networks
Recurrent neural networks
Stability
Two dimensional
吸引力
多重
延迟
盆地
神经元网络
稳定平衡点
稳定性
递归神经网络
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ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/21/7/070701

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Summary:Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation flmctions of 2r （r 〉 1） corner points is studied. Sufficient conditions are established for checking the existence of （2r ＋ 1）2 equilibria in delayed recurrent neural networks. Under these conditions, （r ＋ 1）2 equilibria are locally exponentially stable, and （2r＋ 1）2 -（r ＋ 1）2 -r2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results.
Bibliography:Huang Vu-Jiao, Zhang Hua-Guang, and Wang Zhan-Shan College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
delayed recurrent neural network, multiple equilibria, stability, attractive basin
11-5639/O4
Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation flmctions of 2r （r 〉 1） corner points is studied. Sufficient conditions are established for checking the existence of （2r ＋ 1）2 equilibria in delayed recurrent neural networks. Under these conditions, （r ＋ 1）2 equilibria are locally exponentially stable, and （2r＋ 1）2 -（r ＋ 1）2 -r2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results.
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/21/7/070701