Limit cycles for rigid cubic systems

A. Gasull, Rafel Prohens, J. Torregrosa

Research output: Contribution to journalArticleResearchpeer-review

35 Citations (Scopus)


We consider planar cubic systems with a unique rest point of center-focus type and constant angular velocity. For such systems we obtain an affine classification in three families, and, for two of them, their corresponding phase portraits on the Poincaré sphere. We also prove that for two of these families there is uniqueness of limit cycle. With respect the third family, we give the bifurcation diagram and phase portraits on the Poincaré sphere of a one-parameter sub-family exhibiting at least two limit cycles. © 2004 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)391-404
JournalJournal of Mathematical Analysis and Applications
Publication statusPublished - 15 Mar 2005


  • Bifurcation
  • Center
  • Cubic system
  • Limit cycle


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