On the steadily rotating spirals

Jong Shenq Guo, Ken Ichi Nakamura, Toshiko Ogiwara, Je Chiang Tsai

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalJapan Journal of Industrial and Applied Mathematics
Volume23
Issue number1
DOIs
Publication statusPublished - 2006 Feb

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Keywords

  • Phase plane
  • Spiral wave solution
  • Steadily rotating spiral wave

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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