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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
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.
Received: 20.04.2019 Accepted: 07.07.2019
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
Linking options:
https://www.mathnet.ru/eng/rcd533 https://www.mathnet.ru/eng/rcd/v24/i4/p418
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Abstract page: | 224 | References: | 52 |
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