Numerical study of secondary heteroclinic bifurcations near non-reversible homoclinic snaking

Thorsten Riess

doi:10.3934/proc.2011.2011.1244

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2011, Volume 2011: 1244-1253. Doi: 10.3934/proc.2011.2011.1244 open access

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Numerical study of secondary heteroclinic bifurcations near non-reversible homoclinic snaking

Thorsten Riess^1,

1.
Universität Konstanz, INCIDE, Fach 698, 78457 Konstanz

Received: July 2010

Revised: February 2011

Published: August 2017

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Abstract

We discuss the emergence of isolas of secondary heteroclinic bifurcations near a non-reversible homoclinic snaking curve in parameter space that is generated by a codimension-one equilibrium-to-periodic (EtoP) heteroclinic cycle. We use a numerical method based on Lin's method to compute and continue these secondary heteroclinic EtoP orbits for a well-known system.

Keywords:

Heteroclinic bifurcations,
homoclinic snaking.

Mathematics Subject Classification: Primary: 34C37, 37M20; Secondary: 65L10.

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