Guilin Wen, Jianhua Xie, Daolin Xu
Abstract
An analytical method of the degenerate Hopf bifurcation is proposed for vibro-impact systems. The phenomenon of the bifurcation and its complicated dynamics are observed. This type of bifurcation originates multi-coexisting solutions dependent of the initial state of the system.
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An analytical method of the degenerate Hopf bifurcation is proposed for vibro-impact systems. The phenomenon of the bifurcation and its complicated dynamics are observed. This type of bifurcation originates multi-coexisting solutions dependent of the initial state of the system.
Key concepts: Degenerate energy levels, Hopf bifurcation, Bogdanov–Takens bifurcation, Bifurcation, Saddle-node bifurcation, Transcritical bifurcation, Pitchfork bifurcation, Biological applications of bifurcation theory