Open Access
February 2006 On the Steadily Rotating Spirals
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Je-Chiang Tsai
Japan J. Indust. Appl. Math. 23(1): 1-19 (February 2006).


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.


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Jong-Shenq Guo. Ken-Ichi Nakamura. Toshiko Ogiwara. Je-Chiang Tsai. "On the Steadily Rotating Spirals." Japan J. Indust. Appl. Math. 23 (1) 1 - 19, February 2006.


Published: February 2006
First available in Project Euclid: 19 June 2006

zbMATH: 1103.34035
MathSciNet: MR2210293

Keywords: phase plane , spiral wave solution , steadily rotating spiral wave

Rights: Copyright © 2006 The Japan Society for Industrial and Applied Mathematics

Vol.23 • No. 1 • February 2006
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