Classification of quadratic systems admitting the existence of an algebraic limit cycle

Jaume Llibre, Grzegorz Świrszcz

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

In the paper we find a set of necessary conditions that must be satisfied by a quadratic system in order to have an algebraic limit cycle. We find a countable set of ≤5 parameter families of quadratic systems such that every quadratic system with an algebraic limit cycle must, after a change of variables, belong to one of those families. We provide a classification of all the quadratic systems which can have an algebraic limit cycle based on geometrical properties of the embedding of the system in the Poincaré compactification of R2. We propose names for all the classes we distinguish and we classify all known examples of quadratic systems with algebraic limit cycle. We also prove the integrability of certain classes of quadratic systems. © 2006 Elsevier Masson SAS. All rights reserved.
Original languageEnglish
Pages (from-to)405-421
JournalBulletin des Sciences Mathematiques
Volume131
DOIs
Publication statusPublished - 1 Jul 2007

Keywords

  • Algebraic limit cycles
  • Invariant algebraic curves
  • Quadratic systems

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