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Nelin. Dinam., 2010, Volume 6, Number 2, Pages 255–265 (Mi nd37)  

This article is cited in 2 scientific papers (total in 2 papers)

Visualization of phase trajectories of the Rikitake dynamic system

V. I. Potapov

Norilsk Industrial Institute

Abstract: In paper the computer research of four-dimensional dynamic system with three parameters adequately describing behavior of model coupled Dynamo in view of viscous friction is carried out. Is shown, that in this system there are five equilibrium states: four stable are focuses–node and one is saddle $(3,1)$. Are established the bifurcations of the spatial overwound cycles appropriate to doubling of the period of oscillations dynamic variable and resulting to chaotic oscillations at increase of the relation of factors friction.

Keywords: Rikitake system, equilibrium states, limit cycles, chaos.

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Document Type: Article
UDC: 517.925.41/42
MSC: 70H05, 70K44
Received: 10.01.2010

Citation: V. I. Potapov, “Visualization of phase trajectories of the Rikitake dynamic system”, Nelin. Dinam., 6:2 (2010), 255–265

Citation in format AMSBIB
\Bibitem{Pot10}
\by V.~I.~Potapov
\paper Visualization of phase trajectories of the Rikitake dynamic system
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 2
\pages 255--265
\mathnet{http://mi.mathnet.ru/nd37}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. M. Vodinchar, “Ispolzovanie sobstvennykh mod kolebanii vyazkoi vraschayuscheisya zhidkosti v zadache krupnomasshtabnogo dinamo”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2013, no. 2(7), 33–42  mathnet  crossref  elib
    2. I. A. Ilin, D. S. Noschenko, A. S. Perezhogin, “Dinamicheskie sistemy Rikitaki s treniem”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2013, no. 2(7), 43–45  mathnet  crossref  elib
  • Нелинейная динамика
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