Bifurcations of heteroclinic contours in two-parameter planar systems: Overview and explicit examples

Abstract

Smooth planar vector fields containing two hyperbolic saddles may possess contours formed by heteroclinic connections between these saddles. We present an overview of known results on bifurcations of these contours. Additionally, two new explicit polynomial systems containing such contours are derived, which are studied using the bifurcation software matcont and are shown to exhibit the theoretically predicted phenomena, including series of heteroclinic connections.