Multiplicity of rotating spirals under curvature flows with normal tip motion

Bernold Fiedler, Jong Shenq Guo, Je-Chiang Tsai

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)211-228
Number of pages18
JournalJournal of Differential Equations
Volume205
Issue number1
DOIs
Publication statusPublished - 2004 Oct 1

Fingerprint

Curvature Flow
Multiplicity
Rotating
Spiral Wave
Motion
Givens Rotations
Planar Curves
Excitable Media
Curve
Retract
Global Dynamics
Initial value problems
Number of Solutions
Nonlinear Ordinary Differential Equations
Ordinary differential equations
Wave Front
Initial Value Problem
Circle
Linearly
Curvature

Keywords

  • Energy function
  • Multiplicity
  • Phase plane
  • Spiral wave solution
  • Steadily rotating spiral wave

ASJC Scopus subject areas

  • Analysis

Cite this

Multiplicity of rotating spirals under curvature flows with normal tip motion. / Fiedler, Bernold; Guo, Jong Shenq; Tsai, Je-Chiang.

In: Journal of Differential Equations, Vol. 205, No. 1, 01.10.2004, p. 211-228.

Research output: Contribution to journalArticle

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