Multistability of delayed neural networks with discontinuous activations

Authors:
Xiaofeng Chen;Yafei Zhou;Qiankun Song
Affiliations:
Department of Mathematics, Chongqing Jiaotong University, Chongqing, China;College of Mathematic and Software Science, Sichuan Normal University, Chengdu, China;Department of Mathematics, Chongqing Jiaotong University, Chongqing, China
Venue:
ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
Year:
2010

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Abstract

In the paper, we present the existence of mn locally exponentially stable equilibrium points for a general n-dimensional delayed neural networks with multilevel activation functions which have m segments Furthermore, the theory is also extended to the existence of mn locally exponentially stable limit cycles for the n-dimensional delayed neural networks evoked by periodic external input The results are obtained through formulating parameter conditions, which are easily verifiable and independent of the delay parameter Two numerical examples are given to show the effectiveness of the theory.