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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 1463–1484
DOI: https://doi.org/10.33048/semi.2018.15.120 (Mi semr1008) 		 
Differentical equations, dynamical systems and optimal control

About the whole behavior of trajectories of Darboux systems with cubic nonlinearities

E. P. Volokitinab, V. M. Cheresiza

a Sobolev Institute of Mathematics 4, Acad. Koptyug avenue, Novosibirck, 630090, Russia
b Novosibirsk State University, 2, Pirogova Str., Novosibirck, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2018.15.120
Abstract: We study the local and global behavior of trajectories of the differential systems of the form $\dot x= x+P_3(x,y), \dot y=y+Q_3(x,y)$ where $P_3(x,y)$ and $Q_3(x,y)$ are homogeneous cubic polynomials with a common factor.
Keywords: polynomial systems, singular points, Poincaré equator, phase portraits.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00057_a
Received October 10, 2018, published November 23, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.925
MSC: 34С05
Language: Russian
Citation: E. P. Volokitin, V. M. Cheresiz, “About the whole behavior of trajectories of Darboux systems with cubic nonlinearities”, Sib. Èlektron. Mat. Izv., 15 (2018), 1463–1484
Citation in format AMSBIB
\Bibitem{VolChe18}
\by E.~P.~Volokitin, V.~M.~Cheresiz
\paper About the whole behavior of trajectories of Darboux systems with cubic
nonlinearities
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1463--1484
\mathnet{http://mi.mathnet.ru/semr1008}
\crossref{https://doi.org/10.33048/semi.2018.15.120}
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