中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70701-070701.doi: 10.1088/1674-1056/21/7/070701

• GENERAL • 上一篇    下一篇

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

黄玉娇, 张化光, 王占山   

  1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
  • 收稿日期:2012-01-06 修回日期:2012-02-09 出版日期:2012-06-01 发布日期:2012-06-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008, 61034005, and 61074073), the National Basic Research Program of China (Grant No. 2009CB320601), the Program for New Century Excellent Talents in Universities of China (Grant No. NCET-10-0306), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. N110604005 and N110504001).

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

Huang Yu-Jiao(黄玉娇), Zhang Hua-Guang(张化光)†, and Wang Zhan-Shan(王占山)   

  1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
  • Received:2012-01-06 Revised:2012-02-09 Online:2012-06-01 Published:2012-06-01
  • Contact: Zhang Hua-Guang E-mail:zhanghuaguang@mail.neu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008, 61034005, and 61074073), the National Basic Research Program of China (Grant No. 2009CB320601), the Program for New Century Excellent Talents in Universities of China (Grant No. NCET-10-0306), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. N110604005 and N110504001).

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摘要： Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r≥q1) 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.

关键词: delayed recurrent neural network, multiple equilibria, stability, attractive basin

Abstract: Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r≥q1) 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.

Key words: delayed recurrent neural network, multiple equilibria, stability, attractive basin

中图分类号:  (Neural networks, fuzzy logic, artificial intelligence)

  • 07.05.Mh
02.30.Ks (Delay and functional equations)