Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps

Hüls T (2005)
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 4(4): 985-1007.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper we consider the bifurcation of transversal heteroclinic orbits in discrete time dynamical systems. We assume that a nonhyperbolic transversal heteroclinic orbit exists at some critical parameter value. This situation appears, for example, when one end point undergoes a fold or flip bifurcation. In these two cases the bifurcation analysis of the orbit is performed in detail. In particular, we prove, using implicit function techniques, that the orbit can be continued beyond the bifurcation point. Finally, we show numerical computations for the fold and for the flip bifurcations.
Stichworte
discrete time dynamical systems; continuation; nonhyperbolic transversal heteroclinic orbits; numerical approximation; bifurcation analysis
Erscheinungsjahr
2005
Zeitschriftentitel
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Band
4
Ausgabe
4
Seite(n)
985-1007
ISSN
1536-0040
Page URI
https://pub.uni-bielefeld.de/record/1600913

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Hüls T. Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. 2005;4(4):985-1007.
Hüls, T. (2005). Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 4(4), 985-1007. https://doi.org/10.1137/040614670
Hüls, T. (2005). Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 4, 985-1007.
Hüls, T., 2005. Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 4(4), p 985-1007.
T. Hüls, “Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps”, SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 4, 2005, pp. 985-1007.
Hüls, T.: Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. 4, 985-1007 (2005).
Hüls, Thorsten. “Bifurcation of connecting orbits with one nonhyperbolic fixed point for maps”. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 4.4 (2005): 985-1007.

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