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

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

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume24
Issue number1
DOIs
Publication statusPublished - Jan 2014

Keywords

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

Cite this

Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator. / Cao, Q. J.; Han, Y. W.; Liang, T. W.; Wiercigroch, M.; Piskarev, S.

In: International Journal of Bifurcation and Chaos, Vol. 24, No. 1, 1430005, 01.2014.

Research output: Contribution to journalArticle

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