Multiplicity of rotating spirals under curvature flows with normal tip motion
Multiplicity of rotating spirals under curvature flows with normal tip motion
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具有正常尖端运动的曲率流下旋转螺旋的多重性
DOI：
10.1016/j.jde.2004.02.012
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发表时间：
2004
影响因子：
2.4
通讯作者：
J. Tsai
中科院分区：
文献类型：
--
作者：
B. Fiedler;Jong;J. Tsai
研究了一类二阶自治奇异非线性常微分方程的全局动力学。这个方程来自于可激发介质中稳定旋转螺旋波的模型。尖锐的螺旋波阵面被建模为平面曲线。它们的法向速度被假定为仿射线性地依赖于曲率。螺旋尖端以恒定的旋转频率沿沿着旋转。它既不增长，也不与曲线相切地收缩。以旋转频率为参数，我们通过解析方法得到了该常微分方程初值问题解的整体结构。特别地，可以计算每个给定旋转频率的解的数量。共存的旋转螺旋曲线的重数可以是任何正整数。
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.