Global dynamics of a SD oscillator

Hebai Chen, Jaume Llibre, Yilei Tang

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)


© 2017, Springer Science+Business Media B.V., part of Springer Nature. In this paper, we derive the global bifurcation diagrams of a SD oscillator which exhibits both smooth and discontinuous dynamics depending on the value of a parameter a. We research all possible bifurcations of this system, including Pitchfork bifurcation, degenerate Hopf bifurcation, homoclinic bifurcation, double limit cycle bifurcation, Bautin bifurcation and Bogdanov–Takens bifurcation. Besides, we show that the system has five limit cycles, including four small limit cycles and one large limit cycle. At last, we give all numerical phase portraits to illustrate our results.
Original languageEnglish
Pages (from-to)1755-1777
JournalNonlinear Dynamics
Issue number3
Publication statusPublished - 1 Feb 2018


  • Averaging method
  • Bogdanov–Takens bifurcation
  • Homoclinic loop
  • Hopf bifurcation
  • Limit cycle
  • SD oscillator


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