Upper bounds for the number of limit cycles through linear differential equations

Armengol Gasull, Hector Giacomini

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

Consider the differential equation x = y, y = h0(x)+ h1(x) y+ h2(x) y2 + y3 in the plane. We prove that if a certain solution of an associated linear ordinary differential equation does not change sign, there is an upper bound for the number of limit cycles of the system. The main ingredient of the proof is the Bendixson-Dulac criterion for ℓ-connected sets. Some concrete examples are developed.
Original languageEnglish
Pages (from-to)277-296
JournalPacific Journal of Mathematics
Volume226
DOIs
Publication statusPublished - 1 Aug 2006

Keywords

  • Bendixson-Dulac criterion
  • Limit cycle
  • Linear ordinary differential equation
  • Ordinary differential equation

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