Limit cycles of a second-order differential equation

Ting Chen, Jaume Llibre

Research output: Contribution to journalArticleResearch

2 Citations (Scopus)


© 2018 Elsevier Ltd We provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of ẍ+x=0, when we perturb this system as follows ẍ+ε(1+cosmθ)Q(x,y)+x=0,where ε>0 is a small parameter, m is an arbitrary non-negative integer, Q(x,y) is a polynomial of degree n and θ=arctan(y∕x). The main tool used for proving our results is the averaging theory.
Original languageEnglish
Pages (from-to)111-117
JournalApplied Mathematics Letters
Publication statusPublished - 1 Feb 2019


  • Averaging theory
  • Limit cycle
  • Mathieu–Duffing type


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