Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems

In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented. As an improvement, we obtain by a new method a similar result for a family of quintic polynomia...

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Main Authors:	Ahmed Bendjeddou, Rachid Cheurfa
Format:	Article
Language:	English
Published:	Texas State University 2017-03-01
Series:	Electronic Journal of Differential Equations
Subjects:	Non-algebraic limit cycle invariant curve Poincare return-map first integral Riccati equation
Online Access:	http://ejde.math.txstate.edu/Volumes/2017/71/abstr.html

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spelling	doaj-7409457303af4a41ad14554a9328bcf12020-11-24T22:00:44ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-03-01201771,17Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systemsAhmed Bendjeddou0Rachid Cheurfa1 Univ. de S\etif, Alg\erie Univ. de S\etif, Alg\erie In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented. As an improvement, we obtain by a new method a similar result for a family of quintic polynomial differential systems.http://ejde.math.txstate.edu/Volumes/2017/71/abstr.htmlNon-algebraic limit cycleinvariant curvePoincare return-mapfirst integralRiccati equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Ahmed Bendjeddou Rachid Cheurfa
spellingShingle	Ahmed Bendjeddou Rachid Cheurfa Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems Electronic Journal of Differential Equations Non-algebraic limit cycle invariant curve Poincare return-map first integral Riccati equation
author_facet	Ahmed Bendjeddou Rachid Cheurfa
author_sort	Ahmed Bendjeddou
title	Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
title_short	Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
title_full	Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
title_fullStr	Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
title_full_unstemmed	Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
title_sort	coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2017-03-01
description	In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented. As an improvement, we obtain by a new method a similar result for a family of quintic polynomial differential systems.
topic	Non-algebraic limit cycle invariant curve Poincare return-map first integral Riccati equation
url	http://ejde.math.txstate.edu/Volumes/2017/71/abstr.html
work_keys_str_mv	AT ahmedbendjeddou coexistenceofalgebraicandnonalgebraiclimitcyclesforquinticpolynomialdifferentialsystems AT rachidcheurfa coexistenceofalgebraicandnonalgebraiclimitcyclesforquinticpolynomialdifferentialsystems
_version_	1725842980914331648

Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems

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