Nonautonomous systems with transversal homoclinic structures under discretization

Girod A, Hüls T (2016)
BIT NUMERICAL MATHEMATICS 56(2): 605-631.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Abstract / Bemerkung
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.
Stichworte
Nonautonomous dynamical systems; Homoclinic orbits; Fiber bundles; Discretization effects; Approximation theory; Exponential dichotomy
Erscheinungsjahr
2016
Zeitschriftentitel
BIT NUMERICAL MATHEMATICS
Band
56
Ausgabe
2
Seite(n)
605-631
Konferenz
5th International Conference on Numerical Algebra and Scientific Computing (NASC)
Konferenzort
Shanghai, PEOPLES R CHINA
ISSN
0006-3835
eISSN
1572-9125
Page URI
https://pub.uni-bielefeld.de/record/2917128

Zitieren

Girod A, Hüls T. Nonautonomous systems with transversal homoclinic structures under discretization. BIT NUMERICAL MATHEMATICS. 2016;56(2):605-631.
Girod, A., & Hüls, T. (2016). Nonautonomous systems with transversal homoclinic structures under discretization. BIT NUMERICAL MATHEMATICS, 56(2), 605-631. https://doi.org/10.1007/s10543-015-0567-8
Girod, A., and Hüls, T. (2016). Nonautonomous systems with transversal homoclinic structures under discretization. BIT NUMERICAL MATHEMATICS 56, 605-631.
Girod, A., & Hüls, T., 2016. Nonautonomous systems with transversal homoclinic structures under discretization. BIT NUMERICAL MATHEMATICS, 56(2), p 605-631.
A. Girod and T. Hüls, “Nonautonomous systems with transversal homoclinic structures under discretization”, BIT NUMERICAL MATHEMATICS, vol. 56, 2016, pp. 605-631.
Girod, A., Hüls, T.: Nonautonomous systems with transversal homoclinic structures under discretization. BIT NUMERICAL MATHEMATICS. 56, 605-631 (2016).
Girod, Alina, and Hüls, Thorsten. “Nonautonomous systems with transversal homoclinic structures under discretization”. BIT NUMERICAL MATHEMATICS 56.2 (2016): 605-631.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar