Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator

Q. J. Cao*, Y. W. Han, T. W. Liang, M. Wiercigroch, S. Piskarev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


In this paper, we investigate the global bifurcations and multiple bucklings of a nonlinear oscillator with a pair of strong irrational nonlinear restoring forces, proposed recently by Han et al. [2012]. The equilibrium stabilities of multiple snap-through buckling system under static loading are analyzed. It is found that complex bifurcations are exhibited of codimension-three with two parameters at the catastrophe point. The universal unfolding for the codimension-three bifurcation is also found to be equivalent to a nonlinear viscous damped system. The bifurcation diagrams and the corresponding codimension-three behaviors are obtained by employing subharmonic Melnikov functions for the existing singular closed orbits of homoclinic, tangent homoclinic, homo-heteroclinic and cuspidal heteroclinic, respectively.

Original languageEnglish
Article number1430005
Number of pages17
JournalInternational Journal of Bifurcation and Chaos
Issue number1
Publication statusPublished - Jan 2014


  • Rig-coupled SD oscillator
  • multiple buckling
  • two-parameter codimension-three bifurcation
  • Melnikov's method
  • singular closed orbits
  • discontinuous dynamics
  • archetypal oscillator
  • smooth
  • model
  • parameters


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