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

doi:10.1088/1674-1056/21/7/070701

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.

Keywords: delayed recurrent neural network multiple equilibria stability attractive basin

Received: 06 January 2012
Revised: 09 February 2012
Accepted manuscript online:

PACS:	07.05.Mh	(Neural networks, fuzzy logic, artificial intelligence)
	02.30.Ks	(Delay and functional equations)

Fund: 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).

Corresponding Authors: Zhang Hua-Guang
E-mail: zhanghuaguang@mail.neu.edu.cn

Cite this article:

Huang Yu-Jiao(黄玉娇), Zhang Hua-Guang(张化光), and Wang Zhan-Shan(王占山) Stability and attractive basins of multiple equilibria in delayed two-neuron networks 2012 Chin. Phys. B 21 070701

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

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