Weak center problem and bifurcation of critical periods for a Z-equivariant cubic system
نویسندگان
چکیده
*Correspondence: [email protected] 1Department of Mathematics, Hunan Shaoyang University, Shaoyang, Hunan 422000, P.R. China Full list of author information is available at the end of the article Abstract This paper is devoted to study a center problem and a weak center problem for cubic systems in Z4-equivariant vector fields. By computing the Lyapunov constants and periodic constants carefully, we show that there exit five weak centers of second order, and center conditions and weak center conditions are given for this system. In terms of the problem of multiple weak centers, there are few results studied and thus our work is new and interesting. At the same time, we investigate the critical periodic bifurcation from a weak center.
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