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Globally Attractive Periodic Solutions of Continuous-Time Neural Networks and Their Discrete-Time Counterparts

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Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

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Abstract

In this paper, discrete-time analogues of continuous-time neural networks with continuously distributed delays and periodic inputs are investigated without assuming Lipschitz conditions on the activation functions. The discrete-time analogues are considered to be numerical discretizations of the continuous-time networks and we study their dynamical characteristics. By employing Halanay-type inequality, we obtain easily verifiable sufficient conditions ensuring that every solutions of the discrete-time analogue converge exponentially to the unique periodic solutions. It is shown that the discrete-time analogues inherit the periodicity of the continuous-time networks. The results obtained can be regarded as a generalization to the discontinuous case of previous results established for delayed neural networks possessing smooth neuron activation.

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Author information

Authors and Affiliations

  1. College of Electrical Engineering, Hohai University, Nanjing, 210098, China

    Changyin Sun

  2. Research Institute of Automation, Southeast University, Nanjing, 210096, China

    Changyin Sun, Liangzhen Xia & Chunbo Feng

Authors
  1. Changyin Sun
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  2. Liangzhen Xia
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  3. Chunbo Feng
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Editor information

Editors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  2. The Key Laboratory of Optoelectric Technology & Systems, Ministry of Education, China

    Xiaofeng Liao

  3. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

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© 2005 Springer-Verlag Berlin Heidelberg

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Sun, C., Xia, L., Feng, C. (2005). Globally Attractive Periodic Solutions of Continuous-Time Neural Networks and Their Discrete-Time Counterparts. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_42

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  • DOI: https://doi.org/10.1007/11427391_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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