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Stability properties of traveling pulse solutions of the higher dimensional FitzHugh-Nagumo equations

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Abstract

We consider theN-dimensional FitzHugh-Nagumo (FHN) equations for which there exist planar traveling pulse solutions propagating in the 1-dimensional direction. It is shown that such planar solutions are exponentially stable under small disturbances. The methods used here are the theory ofC o-semigroup and the spectral analysis of the linearized stability criterion for the 1-dimensional FHN equations. Furthermore, we numerically demonstrate how spiral patterns evolve from planar traveling pulses under suitably large disturbances.

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Authors and Affiliations

  1. Hiroshima Junior College of Automotive Engineering, 739-09, Hiroshima, Japan

    Tohru Tsujikawa

  2. Department of Mathematics, Kyushu Institute of Technology, 804, Kitakyushu, Japan

    Toshitaka Nagai

  3. Department of Mathematics, Hiroshima University, 730, Hiroshima, Japan

    Masayasu Mimura

  4. Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University, 520-21, Otsu, Japan

    Ryo Kobayashi

  5. Department of Mathematics, Toyama University, 930, Toyama, Japan

    Hideo Ikeda

Authors
  1. Tohru Tsujikawa
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  2. Toshitaka Nagai
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  3. Masayasu Mimura
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  4. Ryo Kobayashi
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  5. Hideo Ikeda
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Tsujikawa, T., Nagai, T., Mimura, M. et al. Stability properties of traveling pulse solutions of the higher dimensional FitzHugh-Nagumo equations. Japan J. Appl. Math. 6, 341 (1989). https://doi.org/10.1007/BF03167885

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  • DOI: https://doi.org/10.1007/BF03167885

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