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On the steadily rotating spirals

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Abstract

We study an autonomous system of two first order ordinary differential equations. This system arises from a model for steadily rotating spiral waves in excitable media. The sharply located spiral wave fronts are modeled as planar curves. Their normal velocity is assumed to depend affine linearly on curvature. The spiral tip rotates along a circle with a constant positive rotation frequency. The tip neither grows nor retracts tangentially to the curve. With rotation frequency as a parameter, we obtain the complete classification of solutions of this system. Besides providing another approach to derive the results obtained by Fiedler-Guo-Tsai for spirals with positive curvature, we also obtain many more different solutions. In particular, we obtain spiral wave solutions with sign-changing curvature and with negative curvature.

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan Normal University, 88, S-4 Ting Chou Road, 116, Taipei, Taiwan

    Jong -Shenq Guo

  2. Department of Computer Science, University of Electro-Communications, 182-8585, Tokyo, Japan

    Ken -Ichi Nakamura

  3. Department of Mathematics, Josai University, 350-0295, Saitama, Japan

    Toshiko Ogiwara

  4. Department of Computer Science, National Taiwan Ocean University, 2, Pei-Ning Road, 202, Keelung, Taiwan

    Je -Chiang Tsai

Authors
  1. Jong -Shenq Guo
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  2. Ken -Ichi Nakamura
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  3. Toshiko Ogiwara
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  4. Je -Chiang Tsai
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Correspondence to Je -Chiang Tsai.

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Guo, J.S., Nakamura, K.I., Ogiwara, T. et al. On the steadily rotating spirals. Japan J. Indust. Appl. Math. 23, 1 (2006). https://doi.org/10.1007/BF03167495

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  • DOI: https://doi.org/10.1007/BF03167495

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