Limit cycles for a variant of a generalized Riccati equation

Jaume Llibre, Claudia Valls

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


© 2017 Elsevier Ltd In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (ẋ,ẏ=ẍ) given by a variant of the generalized Riccati equation ẍ+εx2n+1ẋ+bx4n+3=0,where b>0, b∈R, n is a non-negative integer and ε is a small parameter. The tool for proving this result uses Abelian integrals.
Original languageEnglish
Pages (from-to)76-79
JournalApplied Mathematics Letters
Publication statusPublished - 1 Jun 2017


  • Abelian integral
  • Generalized Riccati system
  • Limit cycles
  • Weak 16th Hilbert problem


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