E. P. Volokitin, V. M. Cheresiz, “Algebraic limit cycles of planar cubic systems”, Sib. Èlektron. Mat. Izv., 17 (2020), 2045

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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 2045–2054
DOI: https://doi.org/10.33048/semi.2020.17.136 (Mi semr1330)

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

Differentical equations, dynamical systems and optimal control

Algebraic limit cycles of planar cubic systems

E. P. Volokitin^ab, V. M. Cheresiz^a

^a Sobolev Institute of Mathematics 4, Acad. Koptyug ave., Novosibirck, 630090, Russia
^b Novosibirsk State University, 2, Pirogova str., Novosibirck, 630090, Russia

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DOI: https://doi.org/10.33048/semi.2020.17.136

Abstract: We study algebraic limit cycles of differential systems of the form

˙ x = x + P_{3} (x, y), ˙ y = y + Q_{3} (x, y)

$\dot x= x+P_3(x,y), \ \dot y=y+Q_3(x,y)$ where

P_{3} (x, y)

$P_3(x,y)$ and

Q_{3} (x, y)

$Q_3(x,y)$ are homogeneous cubic polynomials.

Keywords: polynomial systems, algebraic limit cycles, non-algebraic limit cycles, phase portraits.

Funding agency	Grant number
Russian Foundation for Basic Research	18-01-00057
Ministry of Science and Higher Education of the Russian Federation	0314-2019-0007 0314-2019-0010
The work is partially supported by RFBR (Grant 18-01-00057). The work was carried out within the state assignment for Sobolev Institute of Mathematics SB RAS (projects 0314-2019-0007, 0314-2019-0010).

Received October 27, 2020, published December 10, 2020

Bibliographic databases:

Document Type: Article

UDC: 517.925

MSC: 34C05

Language: English

Citation: E. P. Volokitin, V. M. Cheresiz, “Algebraic limit cycles of planar cubic systems”, Sib. Èlektron. Mat. Izv., 17 (2020), 2045–2054

Citation in format AMSBIB

\Bibitem{VolChe20}

\by E.~P.~Volokitin, V.~M.~Cheresiz

\paper Algebraic limit cycles of planar cubic systems

\jour Sib. \`Elektron. Mat. Izv.

\yr 2020

\vol 17

\pages 2045--2054

\mathnet{http://mi.mathnet.ru/semr1330}

\crossref{https://doi.org/10.33048/semi.2020.17.136}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000598534700001}

Linking options:

https://www.mathnet.ru/eng/semr1330

https://www.mathnet.ru/eng/semr/v17/p2045

This publication is cited in the following 2 articles:

Jaume Llibre, Claudia Valls, “Polynomial differential systems with hyperbolic limit cycles”, Journal of Geometry and Physics, 194 (2023), 104983
V. M. Cheresiz, E. P. Volokitin, “The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities”, Electron. J. Qual. Theory Differ., 2021, no. 51, 1–12

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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