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Nonnegative Periodic Dynamics of Cohen-Grossberg Neural Networks with Discontinuous Activations and Discrete Time Delays

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Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

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Abstract

In this paper, we report the results concerned with the nonnegative periodic dynamics of the delayed Cohen-Grossberg neural networks with discontinuous activation functions and periodic interconnection coefficients, self-inhibitions, and external inputs. Filippov theory is utilized to study the viability, namely, the existence of the solution of the Cauchy problem. The conditions of diagonal dominant type are presented to guarantee the existence and the asymptotical stability of a periodic solution. Numerical examples are provided to illustrate the theoretical results.

This work was supported by the National Natural Sciences Foundation of China under Grant Nos. 60774074 and 60804044, and sponsored by Shanghai Pujiang Program No. 08PJ14019.

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Authors and Affiliations

  1. Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, 200433, P.R. China

    Xiangnan He, Wenlian Lu & Tianping Chen

Authors
  1. Xiangnan He
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  2. Wenlian Lu
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  3. Tianping Chen
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Editor information

Editors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

    Nian Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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He, X., Lu, W., Chen, T. (2009). Nonnegative Periodic Dynamics of Cohen-Grossberg Neural Networks with Discontinuous Activations and Discrete Time Delays. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_66

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  • DOI: https://doi.org/10.1007/978-3-642-01507-6_66

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

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