Geodesic
Limit cycles from a cubic reversible system via the third-order averaging method
Electronic journal of differential equations, Tome 2015 (2015)
This article concerns the bifurcation of limit cycles from a cubic integrable and non-Hamiltonian system. By using the averaging theory of the first and second orders, we show that under any small cubic homogeneous perturbation, at most two limit cycles bifurcate from the period annulus of the unperturbed system, and this upper bound is sharp. By using the averaging theory of the third order, we show that two is also the maximal number of limit cycles emerging from the period annulus of the unperturbed system.
Classification : 34C07, 37G15, 34C05
Keywords: bifurcation, limit cycles;homogeneous perturbation, averaging method, cubic center, period annulus 
@article{EJDE_2015__2015__a69,
     author = {Peng,  Linping and Feng,  Zhaosheng},
     title = {Limit cycles from a cubic reversible system via the third-order averaging method},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1318.34056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a69/}
}
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AU  - Feng,  Zhaosheng
TI  - Limit cycles from a cubic reversible system via the third-order averaging method
JO  - Electronic journal of differential equations
PY  - 2015
VL  - 2015
UR  - http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a69/
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%A Peng,  Linping
%A Feng,  Zhaosheng
%T Limit cycles from a cubic reversible system via the third-order averaging method
%J Electronic journal of differential equations
%D 2015
%V 2015
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a69/
%G en
%F EJDE_2015__2015__a69
Peng,  Linping; Feng,  Zhaosheng. Limit cycles from a cubic reversible system via the third-order averaging method. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a69/