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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2009, Volume 9, Issue 4, Pages 45–50 (Mi vngu191)  

This article is cited in 4 scientific papers (total in 4 papers)

Relaxations in Singularly Perturbed Planar Systems

L. I. Kononenkoab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: The relaxation oscilations and canard-solutions are studied in the system of singularly perturbed differential equations with one slow and one fast variables. The analysis is based on using classical mathematics, i.e., without elements of nonstandard analysis.
The sufficient condition is presented for the fact that the relaxational oscillation is the limit position of the canard set as the repelling part of the slow manifold tends to zero.

Keywords: singular perturbations, slow and fast variables, slow surface, relaxation oscilations, canard-solutions.

Full text: PDF file (208 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 541.124:541.126:517.9
Received: 17.02.2009

Citation: L. I. Kononenko, “Relaxations in Singularly Perturbed Planar Systems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 9:4 (2009), 45–50

Citation in format AMSBIB
\Bibitem{Kon09}
\by L.~I.~Kononenko
\paper Relaxations in Singularly Perturbed Planar Systems
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2009
\vol 9
\issue 4
\pages 45--50
\mathnet{http://mi.mathnet.ru/vngu191}


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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. L. I. Kononenko, “Pryamaya i obratnaya zadachi dlya singulyarnoi sistemy s medlennymi i bystrymi peremennymi v khimicheskoi kinetike”, Vladikavk. matem. zhurn., 17:1 (2015), 39–46  mathnet
    2. V. P. Golubyatnikov, A. E. Kalenykh, “On structure of phase portraits of some nonlinear dynamical systems”, J. Math. Sci., 215:4 (2016), 475–483  mathnet  crossref
    3. A. E. Gutman, L. I. Kononenko, “Formalizatsiya obratnykh zadach i ee prilozheniya”, Sib. zhurn. chist. i prikl. matem., 17:4 (2017), 49–56  mathnet  crossref
    4. A. E. Gutman, L. I. Kononenko, “Obratnaya zadacha khimicheskoi kinetiki kak kompozitsiya binarnykh sootvetstvii”, Sib. elektron. matem. izv., 15 (2018), 48–53  mathnet  crossref
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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