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

Evgenii Pavlovich Volokitin; Vladimir Mikhaiĭlovich Cheresiz

doi:10.33048/semi.2018.15.120

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

Evgenii Pavlovich Volokitin, Vladimir Mikhaiĭlovich Cheresiz

Higher Mathematics Section

Research output: Contribution to journal › Article › peer-review

Abstract

We study the local and global behavior of trajectories of the differential systems of the form x˙ = x + P₃(x, y); y˙ = y + Q₃(x, y) where P₃(x, y) and Q₃(x, y) are homogeneous cubic polynomials with a common factor.

Translated title of the contribution	О поведении в целом траекторий систем Дарбу с кубическими нелинейностями
Original language	English
Pages (from-to)	1463-1484
Number of pages	22
Journal	Сибирские электронные математические известия
Volume	15
DOIs	https://doi.org/10.33048/semi.2018.15.120
Publication status	Published - 1 Jan 2018

Keywords

polynomial systems
singular points
Poincare equator
phase portraits

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abstract = "We study the local and global behavior of trajectories of the differential systems of the form x˙ = x + P3(x, y); y˙ = y + Q3(x, y) where P3(x, y) and Q3(x, y) are homogeneous cubic polynomials with a common factor.",

keywords = "Phase portraits, Poincar{\'e} equator, Polynomial systems, Singular points, polynomial systems, singular points, Poincare equator, phase portraits",

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AB - We study the local and global behavior of trajectories of the differential systems of the form x˙ = x + P3(x, y); y˙ = y + Q3(x, y) where P3(x, y) and Q3(x, y) are homogeneous cubic polynomials with a common factor.

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KW - Poincaré equator

KW - Polynomial systems

KW - Singular points

KW - polynomial systems

KW - singular points

KW - Poincare equator

KW - phase portraits

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SN - 1813-3304

ER -

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

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Keywords

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