Limit cycles of discontinuous piecewise polynomial vector fields

Tiago de Carvalho, Jaume Llibre, Durval José Tonon

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.
Original languageEnglish
Pages (from-to)572-579
JournalJournal of Mathematical Analysis and Applications
Volume449
Issue number1
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • Averaging theory
  • Cyclicity
  • Limit cycle
  • Piecewise smooth vector fields

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