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  • 标题:Limit cycles in a quartic system with a third-order nilpotent singular point
  • 本地全文:下载
  • 作者:Xinli Li
  • 期刊名称:Advances in Difference Equations
  • 印刷版ISSN:1687-1839
  • 电子版ISSN:1687-1847
  • 出版年度:2018
  • 卷号:2018
  • 期号:1
  • 页码:152
  • DOI:10.1186/s13662-018-1607-x
  • 语种:English
  • 出版社:Hindawi Publishing Corporation
  • 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.
  • 关键词:Quartic system ; Nilpotent critical point ; Lyapunov constants ; Bifurcation of limit cycles
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