Limit cycles for rigid cubic systems

A. Gasull, Rafel Prohens, J. Torregrosa

Research output: Contribution to journalArticleResearchpeer-review

25 Citations (Scopus)

Abstract

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
Volume303
DOIs
Publication statusPublished - 15 Mar 2005

Keywords

  • Bifurcation
  • Center
  • Cubic system
  • Limit cycle

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