Relationships between limit cycles and algebraic invariant curves for quadratic systems

Jaume Llibre, Grzegorz Świrszcz

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

Algebraic limit cycles for quadratic systems started to be studied in 1958. Up to now we know 7 families of quadratic systems having algebraic limit cycles of degree 2, 4, 5 and 6. Here we present some new results on the limit cycles and algebraic limit cycles of quadratic systems. These results provide sometimes necessary conditions and other times sufficient conditions on the cofactor of the invariant algebraic curve for the existence or nonexistence of limit cycles or algebraic limit cycles. In particular, it follows from them that for all known examples of algebraic limit cycles for quadratic systems those cycles are unique limit cycles of the system. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)529-537
JournalJournal of Differential Equations
Volume229
DOIs
Publication statusPublished - 15 Oct 2006

Keywords

  • Algebraic limit cycles
  • Invariant algebraic curves
  • Quadratic systems

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