On the steadily rotating spirals

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2006 Feb
Externally publishedYes


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

ASJC Scopus subject areas

  • General Engineering
  • Applied Mathematics


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