Vorträge und Posterpräsentationen (mit Tagungsband-Eintrag):
A. Steindl:
"Detecting the Shilnikov scenario in a Hopf-Hopf bifurcation with 1:3 resonance";
Vortrag: IUTAM Symposium Analytical Methods in Nonlinear Dynamics,
Frankfurt am Main;
06.07.2015
- 09.07.2015; in: "IUTAM Symposium Analytical Methods in Nonlinear Dynamics",
P. Hagedorn et al. (Hrg.);
Procedia IUTAM/Elsevier,
(2015),
ISSN: 2210-9838;
S. 1
- 8.
Kurzfassung englisch:
We investigate the behaviour of the primary solutions at a Hopf-Hopf interaction close to a 1:3 resonance. It turns out, that the
secondary bifurcations from the primary periodic solution branches are governed by Duffing and Mathieu equations.
By numerical path following a homoclinic orbit at a saddle node was detected, giving rise to the Shilnikov scenario. In order to
understand the creation of homoclinic orbits, a continuation of that orbit was applied, which terminated at an equilibrium with a
triple zero eigenvalue. The existence of different types of homoclinic and heteroclinic orbits in the vicinity of triple zero bifurcation points has already been established. A short discussion of the local bifurcations at the triple zero eigenvalue is given.
Schlagworte:
Hopf-Hopf bifurcation; resonance; Shilnikov scenario; Duffing equation; Mathieu equation; Homoclinic orbit; triple zero eigenvalue
Elektronische Version der Publikation:
http://publik.tuwien.ac.at/files/PubDat_244533.pdf
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.