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

Yu.A. Kuznetsov; J. Hooyman

doi:10.1142/S0218127421300366

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

Yu.A. Kuznetsov, J. Hooyman

Utrecht University

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Article number	2130036
Pages (from-to)	1-20
Number of pages	20
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	31
Issue number	12
Early online date	28 Apr 2021
DOIs	https://doi.org/10.1142/S0218127421300366
Publication status	Published - 30 Sept 2021

Keywords

Connecting orbit
Global bifurcation
Heteroclinic contour
Planar system

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10.1142/S0218127421300366

s0218127421300366Final published version, 3.28 MBLicence: Taverne

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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.",

keywords = "Connecting orbit, Global bifurcation, Heteroclinic contour, Planar system",

author = "Yu.A. Kuznetsov and J. Hooyman",

note = "Funding Information: The authors would like to thank A. V. Dukov (Moscow State University) Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",

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AU - Hooyman, J.

PY - 2021/9/30

Y1 - 2021/9/30

N2 - 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.

AB - 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.

KW - Connecting orbit

KW - Global bifurcation

KW - Heteroclinic contour

KW - Planar system

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ER -

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

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Keywords

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