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Bifurcation and chaos of a vibro-impact system. (Chinese. English summary) Zbl 1340.70018

Summary: From establishing a mechanical model of a three-degree-of-freedom vibro-impact system, we study the Hopf bifurcation and Hopf-flip codimension-two bifurcation of the system based on the Poincaré mapping method. The process of the periodic motion via doubling bifurcation to chaos of the system under different parameters is studied, there exist a quiet complicated unconventionality chaos evolution process and excellent dynamics behaviors, two kinds of unconventionality routes from torus bifurcation and quasi-periodic attractor to chaos are also unfolded.

MSC:

70K50 Bifurcations and instability for nonlinear problems in mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G10 Bifurcations of singular points in dynamical systems
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