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

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

来源：International Journal of Bifurcation and Chaos, 2014, 24(01): 1430005.

DOI：10.1142/s0218127414300055

<jats:p> 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. </jats:p>

• 出版日期2014-1