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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 10, Pages 1809–1821 (Mi zvmmf400)  
This article is cited in 16 scientific papers (total in 16 papers)

Chaos phenomena in a circle of three unidirectionally connected oscillators

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a Faculty of Mathematics, Yaroslavl State University, Sovetskaya ul. 14, Yaroslavl, 150000, Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
Full-text PDF (1513 kB) Citations (16)
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Abstract: A method is proposed for designing chaotic oscillators. Mathematically, three so-called partial oscillators $S_j$ ($j=1,2,3$) are chosen, each of which is modeled by a nonlinear system of ordinary differential equations with a single attractor—an equilibrium or a cycle (the case $S_1=S_ 2=S_3$ is not excluded). It is shown that, when unidirectionally connected in a circle of the form однонаправленно связанными в кольцо вида
$$ \xymatrix{ &S_1\ar[rd]& \\ S_3\ar[ru]&&S_2\ar[ll] } $$
with suitably chosen parameters, these oscillators can exhibit a joint chaotic behavior.
Key words: self-oscillations, oscillators, chaotic attractor, normal form.
Received: 09.03.2006
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 10, Pages 1724–1736
DOI: https://doi.org/10.1134/S0965542506100101
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Chaos phenomena in a circle of three unidirectionally connected oscillators”, Zh. Vychisl. Mat. Mat. Fiz., 46:10 (2006), 1809–1821; Comput. Math. Math. Phys., 46:10 (2006), 1724–1736
Citation in format AMSBIB
\Bibitem{GlyKolRoz06}
\by S.~D.~Glyzin, A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper Chaos phenomena in a~circle of three unidirectionally connected oscillators
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 10
\pages 1809--1821
\mathnet{http://mi.mathnet.ru/zvmmf400}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2304038}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 10
\pages 1724--1736
\crossref{https://doi.org/10.1134/S0965542506100101}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750364305}
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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