Polynomial differential systems with explicit non-algebraic limit cycles

Rebiha Benterki, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)

Abstract

Up to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least exhibiting explicit non-algebraic limit cycles. It is well known that polynomial differential systems of degree 1 (i.e. linear differential systems) has no limit cycles. It remains the open question to determine if the polynomial differential systems of degree 2 can exhibit explicit non-algebraic limit cycles. © 2012 Texas State University - San Marcos.
Original languageEnglish
JournalElectronic Journal of Differential Equations
Volume2012
Publication statusPublished - 15 May 2012

Keywords

  • Non-algebraic limit cycle
  • Polynomial vector field

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