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Regular and Chaotic Dynamics, 2019, Volume 24, Issue 4, Pages 418–431
DOI: https://doi.org/10.1134/S156035471904004X
(Mi rcd533)
 

This article is cited in 5 scientific papers (total in 5 papers)

Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics

Pavel E. Ryabovabc, Artemiy A. Shadrina

a Financial University under the Government of the Russian Federation, Leningradsky prosp. 49, Moscow, 125993 Russia
b Institute of Machines Science, Russian Academy of Sciences, Maly Kharitonyevsky per. 4, Moscow, 101990 Russia
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (5)
References:
Abstract: This article is devoted to the results of phase topology research on a generalized mathematical model, which covers such two problems as the dynamics of two point vortices enclosed in a harmonic trap in a Bose – Einstein condensate and the dynamics of two point vortices bounded by a circular region in an ideal fluid. New bifurcation diagrams are obtained and three-into-one and four-into-one tori bifurcations are observed for some values of the physical parameters of the model. The presence of such bifurcations in the integrable model of vortex dynamics with positive intensities indicates a complex transition and a connection between bifurcation diagrams in both limiting cases. In this paper, we analytically derive equations that define the parametric family of bifurcation diagrams of the generalized model, including bifurcation diagrams of the specified limiting cases. The dynamics of the bifurcation diagram in a general case is shown using its implicit parameterization. A stable bifurcation diagram, related to the problem of dynamics of two vortices bounded by a circular region in an ideal fluid, is observed for particular parameters’ values.
Keywords: completely integrable Hamiltonian system, bifurcation diagram, bifurcation of Liouville tori, dynamics of point vortices, Bose – Einstein condensate.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00846
Ministry of Education and Science of the Russian Federation 1.2404.2017/4.6
The work of P. E.Ryabov was supported by RFBR grant 17-01-00846 and was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (project no. 1.2404.2017/4.6).
Received: 20.04.2019
Accepted: 07.07.2019
Bibliographic databases:
Document Type: Article
Language: English
Citation: Pavel E. Ryabov, Artemiy A. Shadrin, “Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics”, Regul. Chaotic Dyn., 24:4 (2019), 418–431
Citation in format AMSBIB
\Bibitem{RyaSha19}
\by Pavel E. Ryabov, Artemiy A. Shadrin
\paper Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 4
\pages 418--431
\mathnet{http://mi.mathnet.ru/rcd533}
\crossref{https://doi.org/10.1134/S156035471904004X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3989315}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85072904948}
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  • https://www.mathnet.ru/eng/rcd/v24/i4/p418
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:52
     
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