On the steadily rotating spirals

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

研究成果: 雜誌貢獻文章

7 引文 (Scopus)

摘要

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.

原文英語
頁(從 - 到)1-19
頁數19
期刊Japan Journal of Industrial and Applied Mathematics
23
發行號1
DOIs
出版狀態已發佈 - 2006 一月 1

指紋

Spiral Wave
Rotating
Curvature
Planar Curves
Excitable Media
Positive Curvature
Retract
Negative Curvature
First order differential equation
Autonomous Systems
Ordinary differential equations
Wave Front
Circle
Ordinary differential equation
Linearly
Curve
Model

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

引用此文

On the steadily rotating spirals. / Guo, Jong Shenq; Nakamura, Ken Ichi; Ogiwara, Toshiko; Tsai, Je-Chiang.

於: Japan Journal of Industrial and Applied Mathematics, 卷 23, 編號 1, 01.01.2006, p. 1-19.

研究成果: 雜誌貢獻文章

Guo, Jong Shenq ; Nakamura, Ken Ichi ; Ogiwara, Toshiko ; Tsai, Je-Chiang. / On the steadily rotating spirals. 於: Japan Journal of Industrial and Applied Mathematics. 2006 ; 卷 23, 編號 1. 頁 1-19.
@article{75e2c3a089ee4c31a4920fdd6f5e1b28,
title = "On the steadily rotating spirals",
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.",
keywords = "Phase plane, Spiral wave solution, Steadily rotating spiral wave",
author = "Guo, {Jong Shenq} and Nakamura, {Ken Ichi} and Toshiko Ogiwara and Je-Chiang Tsai",
year = "2006",
month = "1",
day = "1",
doi = "10.1007/BF03167495",
language = "English",
volume = "23",
pages = "1--19",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "1",

}

TY - JOUR

T1 - On the steadily rotating spirals

AU - Guo, Jong Shenq

AU - Nakamura, Ken Ichi

AU - Ogiwara, Toshiko

AU - Tsai, Je-Chiang

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

AB - 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.

KW - Phase plane

KW - Spiral wave solution

KW - Steadily rotating spiral wave

UR - http://www.scopus.com/inward/record.url?scp=33645529308&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645529308&partnerID=8YFLogxK

U2 - 10.1007/BF03167495

DO - 10.1007/BF03167495

M3 - Article

AN - SCOPUS:33645529308

VL - 23

SP - 1

EP - 19

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 1

ER -