定常旋转螺旋波运动学模型的分类
Classification of Steadily Rotating Spiral Waves for the Kinematic Model
摘要：
螺旋波出现在许多生物、化学和生理系统中。该运动学模型可用于描述螺旋臂在平面内近似为曲线的运动。对于这个模型，在文献中出现了一些结果。然而，这些结果都是基于对模型的某些简化或对解的先验唯象假设。本文利用完全运动学模型对一类稳定旋转的螺旋波进行了分类，具有正（或负）曲率。事实上，利用我们的结果（定理8），我们可以回答下列问题：对于给定的弱激发介质，是否存在稳定旋转的螺旋波？如果是的话，我们可以知道这些螺旋波的什么样的信息？例如，在一个实施例中，尖端曲率、尖端切向速度和旋转频率。与文献中已有的结果相比，存在一些差异.在简化模型下，只存在曲率单调的解，而在全模型下，则存在曲率任意振荡数的解。
英文摘要：
Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the literature. However, these results all are based upon some simplification on the model or prior phenomenological assumptions on the solutions. In this paper, we use really full kinematic model to classify a generic kind of steadily rotating spiral waves, i.e., with positive (or negative) curvature. In fact, using our results (Theorem 8), we can answer the following questions: Is there any steadily rotating spiral wave for a given weakly excitable medium? If yes, what kind of information we can know about these spiral waves? e.g., the tip's curvature, the tip's tangential velocity, and the rotating frequency. Comparing our results with previous ones in the literature, there are some differences between them. There are only solutions with monotonous curvatures via simplified model but full model admits solutions with any given oscillating number of the curvatures.
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