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Singular Perturbation Approach with Matsuoka Oscillator and Synchronization Phenomena

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Artificial Neural Networks and Machine Learning – ICANN 2011 (ICANN 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6792))

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Abstract

We study the singular perturbation approach in a pair of Matsuoka nonlinear neural oscillators, which consist of membrane potential (v) and recovery (u) dynamics with a relaxation rate (P). This shows that the u-coupled system of the Matsuoka oscillators would be valid for the modeling of neural firings. The coupled integrate-and-fire model of the improved type with an impulse-like interval results from the u-coupled system, under taking the limit of P → ∞, without loss of any coupling properties. We simulate systematically synchronization of both the v-coupled and u-coupled systems. We also discuss potential capabilities of the u-coupled system of Matsuoka oscillators.

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Author information

Authors and Affiliations

  1. Department of Brain Science and Engineering, Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, 2-4, Hibikino, Wakamatsu-ku, Kitakyushu, 808-0196, Japan

    Yasuomi D. Sato, Kazuki Nakada & Kiyotoshi Matsuoka

  2. Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Ruth-Moufang-Str. 1, 60438, Frankfurt am Main, Germany

    Yasuomi D. Sato

Authors
  1. Yasuomi D. Sato
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  2. Kazuki Nakada
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  3. Kiyotoshi Matsuoka
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Editor information

Editors and Affiliations

  1. Department of Information and Computer Science, Aalto University School of Science, P.O. Box 15400, 00076, Aalto, Finland

    Timo Honkela  & Samuel Kaski  & 

  2. School of Physics, Astronomy and Informatics, Department of Informatics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100, Torun, Poland

    Włodzisław Duch

  3. Department of Statistical Science, University College London, 1-19 Torrington Place, WC1E 7HB, London, UK

    Mark Girolami

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© 2011 Springer-Verlag Berlin Heidelberg

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Sato, Y.D., Nakada, K., Matsuoka, K. (2011). Singular Perturbation Approach with Matsuoka Oscillator and Synchronization Phenomena. In: Honkela, T., Duch, W., Girolami, M., Kaski, S. (eds) Artificial Neural Networks and Machine Learning – ICANN 2011. ICANN 2011. Lecture Notes in Computer Science, vol 6792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21738-8_35

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  • DOI: https://doi.org/10.1007/978-3-642-21738-8_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21737-1

  • Online ISBN: 978-3-642-21738-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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