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Dynamical stability analysis of delayed recurrent neural networks with ring structure

College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, P. R. China

The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, P. R. China

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Yujiao Huang

College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, P. R. China

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Tiaoyang Cai

College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, P. R. China

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, and

Zhanshan Wang

College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, P. R. China

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https://doi.org/10.1142/S0217979214501185Cited by:1 (Source: Crossref)

Abstract

In this paper, multistability is discussed for delayed recurrent neural networks with ring structure and multi-step piecewise linear activation functions. Sufficient criteria are obtained to check the existence of multiple equilibria. A lemma is proposed to explore the number and the cross-direction of purely imaginary roots for the characteristic equation, which corresponds to the neural network model. Stability of all of equilibria is investigated. The work improves and extends the existing stability results in the literature. Finally, two examples are given to illustrate the effectiveness of the obtained results.

Keywords:

PACS: 07.05.Mh, 02.30.Ks

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