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Codimension two bifurcation of a vibro-bounce system

【摘要】: <正> A three-degree-of-freedom vibro-bounce systemis considered.The disturbed map of period one single-impactmotion is derived analytically.A center manifold theoremtechnique is applied to reduce the Poincaré map to a three-dimensional one,and the normal form map associated withHopf-flip bifurcation is obtained.Dynamical behavior of thesystem,near the point of codimension two bifurcation,isinvestigated by using qualitative analysis and numerical sim-ulation.It is found that near the point of Hopf-flip bifurcationthere exists not only Hopf bifurcation of period one single-impact motion,but also Hopf bifurcation of period two dou-ble-impact motion.The results from simulation show thatthere exists an interesting torus doubling bifurcation near thecodimension two bifurcation.The torus doubling bifurcationmakes the quasi-periodic attractor associated with period onesingle-impact motion transform to the other quasi-periodicattractor represented by two attracting closed circles.Thetorus bifurcation is qualitatively different from the typicaltorus doubling bifurcation occurring in the vibro-impact sys-tems.Different routes from period one single-impact motionto chaos are observed by numerical simulation.

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