Geodesic
Cubic and quartic planar differential systems with exact algebraic limit cycles
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 34C05, 34A34, 34C25
Keywords: polynomial system, invariant curve, algebraic curve, limit cycle, Hilbert 16th problem 
@article{EJDE_2011__2011__a4,
     author = {Bendjeddou,  Ahmed and Cheurfa,  Rachid},
     title = {Cubic and quartic planar differential systems with exact algebraic limit cycles},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1211.34042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a4/}
}
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AU  - Cheurfa,  Rachid
TI  - Cubic and quartic planar differential systems with exact algebraic limit cycles
JO  - Electronic journal of differential equations
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%A Bendjeddou,  Ahmed
%A Cheurfa,  Rachid
%T Cubic and quartic planar differential systems with exact algebraic limit cycles
%J Electronic journal of differential equations
%D 2011
%V 2011
%U http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a4/
%G en
%F EJDE_2011__2011__a4
Bendjeddou,  Ahmed; Cheurfa,  Rachid. Cubic and quartic planar differential systems with exact algebraic limit cycles. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a4/