scholarly journals Center of planar quintic quasi--homogeneous polynomial differential systems

2015 ◽  
Vol 35 (5) ◽  
pp. 2177-2191 ◽  
Author(s):  
Yilei Tang ◽  
◽  
Long Wang ◽  
Xiang Zhang ◽  
◽  
...  
Keyword(s):  
Homogeneous Polynomial ◽  
Differential Systems ◽  
Polynomial Differential Systems

scholarly journals Planar quasi-homogeneous polynomial differential systems and their integrability

2013 ◽  
Vol 255 (10) ◽  
pp. 3185-3204 ◽  
Author(s):  
Belén García ◽  
Jaume Llibre ◽  
Jesús S. Pérez del Río
Keyword(s):  
Homogeneous Polynomial ◽  
Differential Systems ◽  
Polynomial Differential Systems

Center Problems and Limit Cycle Bifurcations in a Class of Quasi-Homogeneous Systems

2015 ◽  
Vol 25 (10) ◽  
pp. 1550135 ◽  
Author(s):  
Yanqin Xiong ◽  
Maoan Han ◽  
Yong Wang
Keyword(s):  
Limit Cycle ◽  
Differential System ◽  
Homogeneous Polynomial ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
First Order ◽  
Polynomial Differential Systems ◽  
Perturbed System ◽  
Generalized Polynomial ◽  
Necessary And Sufficient

In this paper, we first classify all centers of a class of quasi-homogeneous polynomial differential systems of degree 5. Then we extend this kind of systems to a generalized polynomial differential system and provide the necessary and sufficient conditions to have a center at the origin. Furthermore, we study the Poincaré bifurcation for its perturbed system as it has a center at the origin, find the Poincaré cyclicity up to first order of ε.

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