From chaos to quasi-periodicity

Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tor...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2015-03, Vol.20 (2), p.189-204
Main Authors: Kuznetsov, Alexander P., Migunova, Natalia A., Sataev, Igor R., Sedova, Yuliya V., Turukina, Ludmila V.
Format: Article
Language:English
Subjects:
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
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Summary:Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonance tori are revealed. Boundaries of these domains correspond to the saddle-node bifurcations. Inside the domains of resonance modes, torus-doubling bifurcations and destruction of tori are observed.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354715020070