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BIT Numerical Mathematics

Erschienen in:

01.06.2016

Nonautonomous systems with transversal homoclinic structures under discretization

verfasst von: Alina Girod, Thorsten Hüls

Erschienen in: BIT Numerical Mathematics | Ausgabe 2/2016

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Abstract

We consider homoclinic orbits in continuous time nonautonomous dynamical systems. Unlike the autonomous case, stable and unstable fiber bundles that generalize stable and unstable manifolds, typically intersect transversally in isolated points. In the first part, we establish persistence and error estimates for one-step discretizations of transversal homoclinic orbits. Secondly, we extend an algorithm by England, Krauskopf, Osinga to nonautonomous systems and illustrate transversally intersecting fibers along homoclinic orbits for three examples. The first one is constructed artificially in order to study numerical errors, while the second one is a periodically forced model that reveals the influence of underlying autonomous dynamics. The third example originates from mathematical biology.

Vorheriger Artikel A variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems

Nächster Artikel Analysis and numerical solution of linear delay differential-algebraic equations

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Titel: Nonautonomous systems with transversal homoclinic structures under discretization
verfasst von: Alina Girod
Thorsten Hüls
Publikationsdatum: 01.06.2016
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 2/2016
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-015-0567-8

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