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Section
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Mathematics
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Title
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On Lorenz-like attractors in model of celtic stone
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Author(-s)
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Gonchenko A.S.a
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Affiliations
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Research Institute for Applied Mathematics and Cybernetics, Nizhni Novgorod State Universitya
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Abstract
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We study chaotic dynamics in a nonholonomic model of celtic stone. We show that, for certain values of parameters characterizing geometrical and physical properties of the stone, a strange Lorenz-like attractor is observed in the model. We study certain steps of appearance and break-down of this attractor.
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Keywords
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celtic stone, nonholonomic model, Lorenz-like attractor, chaotic dynamics
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UDC
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517.925, 517.3
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MSC
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37J60, 37N15, 37G35
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DOI
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10.20537/vm130201
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Received
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25 April 2013
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Language
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Russian
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Citation
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Gonchenko A.S. On Lorenz-like attractors in model of celtic stone, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 2, pp. 3-11.
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References
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- Borisov A.V., Mamaev I.S. Strange attractors in rattleback dynamics, Nonholonomic dynamical systems, Moscow–Izhevsk: RCD, 2002, pp. 293–316.
- Borisov A.V., Mamaev I.S. Strange attractors in rattleback dynamics, Advances in Physic Sciences, 2003, vol. 117, no. 4, pp. 407–418.
- Gonchenko A.S., Gonchenko S.V., Kazakov A.O. On new aspects of celtic stone chaotic dynamics, Nelin. Dinamika, 2012, vol. 8, no. 3, pp. 507–518.
- Kuznetsov S.P., Zhalnin A.Yu., Sataev I.R., Sedova Yu.V. Phenomena of nonlinear dynamics of dissipative systems in nonholonomic mechanics of the rattleback, Nelin. Dinamika, 2012, vol. 8, no. 4, pp. 735–762.
- Delshams A., Gonchenko S.V., Gonchenko V.S., Lazaro J.T. and Sten’kin O.V. Abundance of attracting, repelling and elliptic orbits in two-dimensional reversible maps, Nonlinearity, 2013, vol. 26, no. 1, pp. 1–35.
- Gonchenko S.V., Ovsyannikov I.I., Simo C., Turaev D. Three-dimensional Henon-like maps and wild Lorenz-like attractors, Int. J. Bifurcation and Chaos, 2005, vol. 15, pp. 3493–3508.
- Plykin R.V., Sataev E.A., Shlyachkov S.V. Strange attractors, Dynamical systems–9, red. Anosov D.V., Moscow: VINITI, 1999, pp. 100–148.
- Shilnikov L.P. The bifurcation theory and turbulence, Methods of qualitative theory of differential equations, Gor’kii: Gor’kov. Gos. Univ., 1986, pp. 150–163.
- Gonchenko A.S., Gonchenko S.V., Shilnikov L.P. Towards scenarios of chaos appearance in three-dimensional maps, Nelin. Dinamika, 2012, vol. 8, no. 1, pp. 3–28.
- Borisov A.V., Mamaev I.S. Dinamika tverdogo tela (Rigid body dynamics), Moscow–Izhevsk: RCD, 2001, 384 p.
- Shilnikov L.P. The bifurcation theory and the Lorenz model, Bifurcation of the cycle and its applications, Moscow: Mir, 1980, pp. 317–335.
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