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

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 Poincaré index, and supplementing a function for discriminating the limit cycle from other closed streamlines, our algorithm obtains much better results than Wischgoll's.