Multiplicity of rotating spirals under curvature flows with normal tip motion

Bernold Fiedler, Jong Shenq Guo, Je Chiang Tsai

研究成果: 雜誌貢獻文章

8 引文 斯高帕斯(Scopus)

摘要

We study the global dynamics of a singular nonlinear ordinary differential equation, which is autonomous of second order. This equation 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 rotation frequency. It neither grows nor retracts tangentially to the curve. With rotation frequency as a parameter, we derive the global structure of solutions of the associated initial value problem for this ODE, by an analytical approach. In particular, the number of solutions for each given rotation frequency can be computed. The multiplicity of coexisting rotating spiral curves can be any positive integer.

原文英語
頁(從 - 到)211-228
頁數18
期刊Journal of Differential Equations
205
發行號1
DOIs
出版狀態已發佈 - 2004 十月 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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