Codim 2 bifurcations of planar heteroclinic contours

Abstract

Smooth planar vector fields containing two hyperbolic saddles may contain contours formed by heteroclinic connections between these saddles. This thesis presents an overview of the bifurcations of these contours based on publications by J.W. Reyn and A. Dukov. Using truncated correspondence maps, all relevant bifurcations diagrams are rederived. Additionally, two new explicit polynomial systems containing such contours are derived which are studied using the bifurcation software Matcont.