Global phase portraits of the generalized van der Pol systems

Jaume Llibre, Claudia Valls*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We consider the generalized van der Pol systems x˙=y,y˙=−x+(1−x2)f(y), where f∈R[y]. The classical van der Pol systems have f(y)=y. We first characterize when the origin of the generalized van der Pol systems is a center, and second we provide the global phase portraits in the Poincaré disc of the generalized van der Pol when f(y)=a1y+a2y2 for all a1,a2∈R.

Original languageEnglish
Article number103213
Number of pages19
JournalBulletin des Sciences Mathematiques
Volume182
DOIs
Publication statusPublished - Feb 2023

Keywords

  • Blow ups
  • Center
  • Lyapunov constant
  • Poincaré compactification
  • van der Pol systems

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