Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves

In this article we consider a class of quadratic polynomial differential systems in the plane having a hyperbola and a straight line as invariant algebraic curves, and we classify all its phase portraits. Moreover these systems are integrable and we provide their first integrals.

Bibliographic Details
Main Authors:	Jaume Llibre, Jiang Yu
Format:	Article
Language:	English
Published:	Texas State University 2018-07-01
Series:	Electronic Journal of Differential Equations
Subjects:	Quadratic system, first integral, global phase portraits, invariant hperbola, invariant straight line
Online Access:	http://ejde.math.txstate.edu/Volumes/2018/141/abstr.html

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spelling	doaj-f9686a69bc564585a5230787299263642020-11-25T01:49:36ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-07-012018141,119Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curvesJaume Llibre0Jiang Yu1 Univ. Autonoma de Barcelona, Catalonia, Spain Shanghai Jiao Tong Univ., Shanghai, China In this article we consider a class of quadratic polynomial differential systems in the plane having a hyperbola and a straight line as invariant algebraic curves, and we classify all its phase portraits. Moreover these systems are integrable and we provide their first integrals.http://ejde.math.txstate.edu/Volumes/2018/141/abstr.htmlQuadratic system, first integral, global phase portraits, invariant hperbola, invariant straight line
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jaume Llibre Jiang Yu
spellingShingle	Jaume Llibre Jiang Yu Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves Electronic Journal of Differential Equations Quadratic system, first integral, global phase portraits, invariant hperbola, invariant straight line
author_facet	Jaume Llibre Jiang Yu
author_sort	Jaume Llibre
title	Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves
title_short	Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves
title_full	Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves
title_fullStr	Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves
title_full_unstemmed	Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves
title_sort	global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2018-07-01
description	In this article we consider a class of quadratic polynomial differential systems in the plane having a hyperbola and a straight line as invariant algebraic curves, and we classify all its phase portraits. Moreover these systems are integrable and we provide their first integrals.
topic	Quadratic system, first integral, global phase portraits, invariant hperbola, invariant straight line
url	http://ejde.math.txstate.edu/Volumes/2018/141/abstr.html
work_keys_str_mv	AT jaumellibre globalphaseportraitsforquadraticsystemswithahyperbolaandastraightlineasinvariantalgebraiccurves AT jiangyu globalphaseportraitsforquadraticsystemswithahyperbolaandastraightlineasinvariantalgebraiccurves
_version_	1725006342344671232

Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves

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