Limit cycles in a quartic system with a third-order nilpotent singular point

被引：2

作者：

Li, Xinli ^{[1
,2
]}

机构：

[1] Univ Shanghai Sci & Technol, Sch Business, Shanghai, Peoples R China

[2] Linyi Univ, Logist Sch, Linyi, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2018年

关键词：

Quartic system; Nilpotent critical point; Lyapunov constants; Bifurcation of limit cycles; LYAPUNOV SYSTEM; HAMILTONIAN-SYSTEMS; BIFURCATIONS; CENTERS;

D O I：

10.1186/s13662-018-1607-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, limit cycles bifurcating from a third-order nilpotent critical point in a class of quartic planar systems are studied. With the aid of computer algebra system MAPLE, the first 12 Lyapunov constants are deduced by the normal form method. As a result, sufficient and necessary center conditions are derived, and the fact that there exist 12 or 13 limit cycles bifurcating from the nilpotent critical point is proved by different perturbations. The result in [Qiu et al. in Adv. Differ. Equ. 2015(1):1, 2015] is improved.

引用

页数：15

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