Restricted independence in displacement function for better estimation of cyclicity

Xingwu Chen, Jaume Llibre, Zhaoxia Wang, Weinian Zhang

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


© 2017 Elsevier Inc. Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. We apply this method to a nondegenerate cubic center-focus variety and prove that the cyclicity reaches its an upper bound.
Original languageEnglish
Pages (from-to)5773-5791
JournalJournal of Differential Equations
Issue number12
Publication statusPublished - 15 Jun 2017


  • Center-focus variety
  • Cyclicity
  • Focal value
  • Independence
  • Power sequence


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