Bifurcations of heteroclinic contours in two-parameter planar systems: Overview and explicit examples
Dynamical Systems
2023-03-01 v3
Abstract
Smooth planar vector fields containing two hyperbolic saddles may possess contours formed by heteroclinic connections between these saddles. We present an overview of the bifurcations of these contours based on papers by J.W. Reyn and A.V. Dukov. 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.
Cite
@article{arxiv.2103.14742,
title = {Bifurcations of heteroclinic contours in two-parameter planar systems: Overview and explicit examples},
author = {Yuri A. Kuznetsov and Joost Hooyman},
journal= {arXiv preprint arXiv:2103.14742},
year = {2023}
}
Comments
Corrected published version, 20 pages, 25 figures, added references