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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 2, Pages 189–204
DOI: https://doi.org/10.1134/S1560354715020070 (Mi rcd53) 		 
This article is cited in 19 scientific papers (total in 19 papers)

From Chaos to Quasi-Periodicity

Alexander P. Kuznetsovab, Natalia A. Migunovab, Igor R. Sataeva, Yuliya V. Sedovaa, Ludmila V. Turukinaab

a Kotel’nikov Institute of Radio Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019 Russia
b Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia
Citations (19)
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DOI: https://doi.org/10.1134/S1560354715020070
Abstract: 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.
Keywords: chaos, quasi-periodic oscillation, invariant torus, Lyapunov exponent, bifurcation.
Funding agency Grant number
Russian Foundation for Basic Research 14-02-00085
Ministry of Education and Science of the Russian Federation NSh-1726.2014
This work was supported by the Russian Foundation for Basic Research grant No.14-02-00085 and by RF Presidential program for leading Russian research schools NSh-1726.2014.
Received: 19.01.2015
Bibliographic databases:
Document Type: Article
MSC: 70K43, 65P20, 65P30, 34D08
Language: English
Citation: Alexander P. Kuznetsov, Natalia A. Migunova, Igor R. Sataev, Yuliya V. Sedova, Ludmila V. Turukina, “From Chaos to Quasi-Periodicity”, Regul. Chaotic Dyn., 20:2 (2015), 189–204
Citation in format AMSBIB
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\paper From Chaos to Quasi-Periodicity
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 189--204
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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