Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve

Jeidy J. Jimenez, Jaume Llibre*, João C. Medrado

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

As for the general planar differential systems one of the main problems for the piecewise linear differential systems is to determine the existence and the maximum number of crossing limits cycles that these systems can exhibit. But in general to provide a sharp upper bound on the number of crossing limit cycles is a very difficult problem. In this work we study the existence of crossing limit cycles and their distribution for piecewise linear differential systems formed by linear differential centers and separated by a reducible cubic curve, formed either by a circle and a straight line, or by a parabola and a straight line.

Original languageEnglish
Article number19
Number of pages48
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2020
DOIs
Publication statusPublished - 2020

Keywords

  • Conics
  • Discontinuous piecewise linear differential centers
  • Limit cycles

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