### 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 language | English |
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Pages (from-to) | 211-228 |

Number of pages | 18 |

Journal | Journal of Differential Equations |

Volume | 205 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 Oct 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Analysis

### Cite this

*Journal of Differential Equations*,

*205*(1), 211-228. https://doi.org/10.1016/j.jde.2004.02.012

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

Research output: Contribution to journal › Article

*Journal of Differential Equations*, vol. 205, no. 1, pp. 211-228. https://doi.org/10.1016/j.jde.2004.02.012

}

TY - JOUR

T1 - Multiplicity of rotating spirals under curvature flows with normal tip motion

AU - Fiedler, Bernold

AU - Guo, Jong Shenq

AU - Tsai, Je-Chiang

PY - 2004/10/1

Y1 - 2004/10/1

N2 - 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.

AB - 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.

KW - Energy function

KW - Multiplicity

KW - Phase plane

KW - Spiral wave solution

KW - Steadily rotating spiral wave

UR - http://www.scopus.com/inward/record.url?scp=4344580148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344580148&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2004.02.012

DO - 10.1016/j.jde.2004.02.012

M3 - Article

AN - SCOPUS:4344580148

VL - 205

SP - 211

EP - 228

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -