Geodesic
Bifurcation of limit cycles from quartic isochronous systems
Electronic journal of differential equations, Tome 2014 (2014)
This article concerns the bifurcation of limit cycles for a quartic system with an isochronous center. By using the averaging theory, it shows that under any small quartic homogeneous perturbations, at most two limit cycles bifurcate from the period annulus of the considered system, and this upper bound can be reached. In addition, we study a family of perturbed isochronous systems and prove that there are at most three limit cycles bifurcating from the period annulus of the unperturbed one, and the upper bound is sharp.
Classification : 34C07, 37G15, 34C05
Keywords: bifurcation, limit cycles, homogeneous perturbation, averaging method, isochronous center, period annulus 
@article{EJDE_2014__2014__a95,
     author = {Peng,  Linping and Feng,  Zhaoshen},
     title = {Bifurcation of limit cycles from quartic isochronous systems},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1417.34075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a95/}
}
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TI  - Bifurcation of limit cycles from quartic isochronous systems
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
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%A Feng,  Zhaoshen
%T Bifurcation of limit cycles from quartic isochronous systems
%J Electronic journal of differential equations
%D 2014
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%G en
%F EJDE_2014__2014__a95
Peng,  Linping; Feng,  Zhaoshen. Bifurcation of limit cycles from quartic isochronous systems. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a95/