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Nelin. Dinam., 2010, Volume 6, Number 2, Pages 241–254 (Mi nd36)  

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

On investigation of resonances in system of two Duffing–van der Pol equations

R. E. Kondrashov, A. D. Morozov

State University of Nizhni Novgorod

Abstract: We consider a problem about interaction of the two Duffing–van der Pol equations close to nonlinear integrable. The average systems describing behaviour of the solutions of the initial equation in resonant zones are deduced. The conditions of existence of not trivial resonant structures are established. The results of research in cases are resulted, when at the uncoupled equations exist and there are no limiting cycles.

Keywords: limit cycles, resonances.

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Document Type: Article
UDC: 517.9:534.1
MSC: 34C15
Received: 29.03.2010

Citation: R. E. Kondrashov, A. D. Morozov, “On investigation of resonances in system of two Duffing–van der Pol equations”, Nelin. Dinam., 6:2 (2010), 241–254

Citation in format AMSBIB
\Bibitem{KonMor10}
\by R.~E.~Kondrashov, A.~D.~Morozov
\paper On investigation of resonances in system of two Duffing--van~der~Pol equations
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 2
\pages 241--254
\mathnet{http://mi.mathnet.ru/nd36}
\elib{http://elibrary.ru/item.asp?id=15002231}


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    This publication is cited in the following articles:
    1. R. E. Kondrashov, A. D. Morozov, “O globalnom povedenii reshenii sistemy dvukh uravnenii Dyuffinga – Van der Polya”, Nelineinaya dinam., 7:3 (2011), 437–449  mathnet
    2. Barabanov I.N., Tkhai V.N., “A Family of Oscillations in the Model Containing Coupled Subsystems”, Proceedings of 2016 International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy'S Conference), ed. Tkhai V., IEEE, 2016  isi
    3. V. N. Tkhai, “Model containing coupled subsystems with oscillations of different types”, Autom. Remote Control, 78:4 (2017), 595–607  mathnet  crossref  mathscinet  isi  elib
    4. I. N. Barabanov, V. N. Tkhai, “Stabilization of oscillations in a periodic system by choosing appropriate couplings”, Autom. Remote Control, 79:12 (2018), 2128–2135  mathnet  crossref  crossref  isi  elib
    5. V. N. Tkhai, “Periodicheskaya model, soderzhaschaya svyazannye podsistemy s razlichnymi tipami kolebanii”, Avtomat. i telemekh., 2019, no. 3, 55–67  mathnet  crossref  elib
  • Нелинейная динамика
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