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| Anti-controlling Period-doubling Bifurcation of an Inertial Impact Shaker System |
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Abstract In the premise of no change of periodic solutions of the original system and with consideration of the difficulties that given by the implicit Poincaré map of the impact shaker system and the classical critical criterion of mapping period-doubling bifurcation described by the properties of eigenvalues, the method of anti-control of period-doubling bifurcation of an inertial impact shaker system is proposed on basis of an explicit critical criterion without using eigenvalues calculation. Firstly, the linear feedback control is used to deduce the Poincaré map of close-loop system, and the period-doubling bifurcation explicit critical criterion without using eigenvalues calculation is applied to obtain the controlling parameters area. Then, the stability of the period-doubling bifurcation is further analyzed by utilizing the center manifold and normal formal theory. The ultimate numerical experiments verify that the stable period-doubling bifurcation solutions can be generated at an arbitrary specified parameters point by controlling.
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Received: 04 May 2014
Published: 28 February 2014
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2015, Vol. 36 
