Volume 9, Number 5, 2019, Pages 19011926 DOI：10.11948/20190005 
Local bifurcation of critical periods in quadraticlike cubic systems 
Zhiheng Yu,Zhaoxia Wang 
Keywords:Quadraticlike cubic systems, critical period bifurcation, pseudo division, variety decomposition. 
Abstract: 
In this paper, we investigate quadraticlike cubic systems having a center at $O$ for the local bifurcation of critical periods. We provide an inductive algorithm to compute polynomials of periodic coefficients, find structures of solutions for systems of algebraic equations corresponding to weak centers of finite order, and derive conditions on parameters under which the considered equilibrium is a weak center of order $k$, $k=0,1,2,3,4$. Furthermore, we show that with appropriate perturbations, at most four critical periods bifurcate from the weak center of finite order, and we give conditions under which exactly $k$ critical periods bifurcate from the center $O$ for each integer $k=1,2,3,4$. 
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