Cyclicity of a fake saddle inside the quadratic vector fields

P. De Maesschalck, S. Rebollo-Perdomo, J. Torregrosa

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


© 2014 Elsevier Inc. This paper concerns the study of small-amplitude limit cycles that appear in the phase portrait near an unfolded fake saddle singularity. This degenerate singularity is also known as an impassable grain. The canonical form of the unperturbed vector field is like a degenerate flow box. Near the singularity, the phase portrait consists of parallel fibers, all but one of which have no singular points, and at the singular fiber, there is one node. We demonstrate different techniques in order to show that the cyclicity is bigger than or equal to two when the canonical form is quadratic.
Original languageEnglish
Pages (from-to)588-620
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - 1 Jan 2015


  • Bifurcation
  • Cyclicity
  • Fake saddle
  • Impassable grain
  • Limit cycle
  • Singularity unfolding


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