Cubic and quartic planar differential systems with exact algebraic limit cycles

Cubic and quartic planar differential systems with exact algebraic limit cycles

We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems wit...

Full description

Bibliographic Details
Main Authors: Ahmed Bendjeddou, Rachid Cheurfa
Format: Article
Language:English
Published: Texas State University 2011-01-01
Series:Electronic Journal of Differential Equations
Subjects:
Polynomial system
invariant curve
algebraic curve
limit cycle
Hilbert 16th problem
Online Access:http://ejde.math.txstate.edu/Volumes/2011/15/abstr.html
id doaj-624468e14346466e96e2bfa7f56da578
record_format Article
spelling doaj-624468e14346466e96e2bfa7f56da5782020-11-24T23:38:56ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-01-01201115,112Cubic and quartic planar differential systems with exact algebraic limit cyclesAhmed BendjeddouRachid CheurfaWe construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems with four algebraic limit cycles and another for which nested configurations of limit cycles occur. http://ejde.math.txstate.edu/Volumes/2011/15/abstr.htmlPolynomial systeminvariant curvealgebraic curvelimit cycleHilbert 16th problem
collection DOAJ
language English
format Article
sources DOAJ
author Ahmed Bendjeddou
Rachid Cheurfa
spellingShingle Ahmed Bendjeddou
Rachid Cheurfa
Cubic and quartic planar differential systems with exact algebraic limit cycles
Electronic Journal of Differential Equations
Polynomial system
invariant curve
algebraic curve
limit cycle
Hilbert 16th problem
author_facet Ahmed Bendjeddou
Rachid Cheurfa
author_sort Ahmed Bendjeddou
title Cubic and quartic planar differential systems with exact algebraic limit cycles
title_short Cubic and quartic planar differential systems with exact algebraic limit cycles
title_full Cubic and quartic planar differential systems with exact algebraic limit cycles
title_fullStr Cubic and quartic planar differential systems with exact algebraic limit cycles
title_full_unstemmed Cubic and quartic planar differential systems with exact algebraic limit cycles
title_sort cubic and quartic planar differential systems with exact algebraic limit cycles
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2011-01-01
description We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems with four algebraic limit cycles and another for which nested configurations of limit cycles occur.
topic Polynomial system
invariant curve
algebraic curve
limit cycle
Hilbert 16th problem
url http://ejde.math.txstate.edu/Volumes/2011/15/abstr.html
work_keys_str_mv AT ahmedbendjeddou cubicandquarticplanardifferentialsystemswithexactalgebraiclimitcycles
AT rachidcheurfa cubicandquarticplanardifferentialsystemswithexactalgebraiclimitcycles
_version_ 1725515361218985984

Similar Items