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This article is cited in 3 scientific papers (total in 3 papers)
Dynamics of small perturbations of orbits on a torus in a quasiperiodically forced 2D dissipative map
A. Yu. Jalninea, S. P. Kuznetsovba, A. Osbaldestinc a Institute of Radio-Engineering
and Electronics, RAS, Saratov Branch
Zelenaya 38, 410019 Saratov, Russia
b Max-Planck-Institut für Physik Komplexer Systeme
Nöthnitzer Straße 38, 01187 Dresden, Germany
c University of Portsmouth,
Portsmouth, PO1 3HE, UK
Abstract:
We consider the dynamics of small perturbations of stable two-frequency quasiperiodic orbits on an attracting torus in the quasiperiodically forced Hénon map. Such dynamics consists in an exponential decay of the radial component and in a complex behaviour of the angle component. This behaviour may be two- or three-frequency quasiperiodicity, or it may be irregular. In the latter case a graphic image of the dynamics of the perturbation angle is a fractal object, namely a strange nonchaotic attractor, which appears in auxiliary map for the angle component. Therefore, we claim that stable trajectories may approach the attracting torus either in a regular or in an irregular way. We show that the transition from quasiperiodic dynamics to chaos in the model system is preceded by the appearance of an irregular behaviour in the approach of the perturbed quasiperiodic trajectories to the smooth attracting torus. We also demonstrate a link between the evolution operator of the perturbation angle and a quasiperiodically forced circle mapping of a special form and with a Harper equation with quasiperiodic potential.
Keywords:
quasiperiodicity, strange nonchaotic attractor, bifurcation, stability analysis.
Received: 13.10.2005 Accepted: 25.12.2005
Citation:
A. Yu. Jalnine, S. P. Kuznetsov, A. Osbaldestin, “Dynamics of small perturbations of orbits on a torus in a quasiperiodically forced 2D dissipative map”, Regul. Chaotic Dyn., 11:1 (2006), 19–30
Linking options:
https://www.mathnet.ru/eng/rcd655 https://www.mathnet.ru/eng/rcd/v11/i1/p19
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