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Regul. Chaotic Dyn., 2015, Volume 20, Issue 2, Pages 189–204 (Mi rcd53)  

This article is cited in 7 scientific papers (total in 7 papers)

From Chaos to Quasi-Periodicity

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

a Kotelínikov 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

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.


DOI: https://doi.org/10.1134/S1560354715020070

References: PDF file   HTML file

Bibliographic databases:

MSC: 70K43, 65P20, 65P30, 34D08
Received: 19.01.2015
Language:

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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\by Alexander P. Kuznetsov, Natalia A. Migunova, Igor R. Sataev, Yuliya V. Sedova, Ludmila V. Turukina
\paper From Chaos to Quasi-Periodicity
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 189--204
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\crossref{https://doi.org/10.1134/S1560354715020070}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sergey P. Kuznetsov, “Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models”, Regul. Chaotic Dyn., 20:3 (2015), 345–382  mathnet  crossref  mathscinet  zmath  adsnasa
    2. S. Das, Ch. B. Dock, Y. Saiki, M. Salgado-Flores, E. Sander, J. Wu, J. A. Yorke, “Measuring quasiperiodicity”, EPL, 114:4 (2016), 40005  crossref  isi  scopus
    3. S. P. Kuznetsov, V. P. Kruglov, “On some simple examples of mechanical systems with hyperbolic chaos”, Proc. Steklov Inst. Math., 297 (2017), 208–234  mathnet  crossref  crossref  mathscinet  isi  elib
    4. S. Das, Y. Saiki, E. Sander, J. A. Yorke, “Quantitative quasiperiodicity”, Nonlinearity, 30:11 (2017), 4111–4140  crossref  mathscinet  zmath  isi  scopus
    5. B. C. Bao, P. Y. Wu, H. Bao, Q. Xu, M. Chen, “Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in third-order autonomous memristive oscillator”, Chaos Solitons Fractals, 106 (2018), 161–170  crossref  mathscinet  isi  scopus
    6. A. P. Kuznetsov, S. P. Kuznetsov, N. A. Shchegoleva, N. V. Stankevich, “Dynamics of coupled generators of quasiperiodic oscillations: different types of synchronization and other phenomena”, Physica D, 398 (2019), 1–12  crossref  mathscinet  isi  scopus
    7. N. Stankevich, A. Kuznetsov, E. Popova, E. Seleznev, “Chaos and hyperchaos via secondary Neimark–Sacker bifurcation in a model of radiophysical generator”, Nonlinear Dyn., 97:4 (2019), 2355–2370  crossref  zmath  isi  scopus
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