利用临界点聚类的平面向量场极限环的检出及可视化

A Critical Point Clustering Approach to Detection and Visualization of Limit Cycles in Planar Vector Fields

检出和可视化极限环已经成为向量场拓扑分析中日益重要的研究课题.提出了一个基于临界点聚类的检出算法,将向量场的全部临界点以几何距离为相似性判据聚类成一棵二叉树,通过只检查临界点指数和为+1的少数树结点,以及在算法中增加检测和剔除中心型闭轨的部分,获得了比Wischgoll算法更好的结果.

Detection and visualization of the limit cycle has become an increasingly attractive research topic in vector field topological analysis. In 2001, Wischgoll and Scheuermann proposed an algorithm for detection and visualization of the limit cycle in planar vector fields. However, since no discrimination from other closed streamlines is taken into consideration, accumulated errors from streamline integration could produce wrong detection. In this paper, we present a critical point clustering based algorithm. By the algorithm, through clustering all the critical points into a binary tree, investigating only the tree nodes with ＋ 1 Poincare index, and supplementing a function for discriminating the limit cycle from other closed streamlines, our algorithm obtains much better results than Wischgoll＇s.