Detecting and visualizing local bifurcations in 2D time-dependent vector fields

In this paper, we present a new approach to detecting, locating and visualizing the local bifurcations originated from the changes of critical points in a 2D time-dependent vector field. Via precisely tracking the changes of all the critical points in a flow and pictorially displaying the evolution paths of these changes with a color model, our method can find and visualize all of this kind of bifurcations. This work extends Theisel´s research on detecting a few local bifurcations based on the feature flow fields, and provides more complete information for probing into the structural instability in complex flow fields.