Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Jaume Llibre, Bruno D. Lopes, Jaime R. De Moraes

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)

Abstract

We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers (Formula presented.) when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems with two zones of discontinuity separated by a straight line. We obtain that this number is 3 for the perturbed continuous systems and at least 12 for the discontinuous ones using the averaging method of first order. © 2014 Springer Basel.
Original languageEnglish
Pages (from-to)129-148
JournalQualitative Theory of Dynamical Systems
Volume13
Issue number1
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Averaging method
  • Isochronous center
  • Limit cycle
  • Periodic orbit
  • Polynomial vector field

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