Bifurcations in impact systems
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Cited by (73)
Resonant periodic solutions in regularized impact oscillator
2021, Journal of Mathematical Analysis and ApplicationsPeriodic motions generated from non-autonomous grazing dynamics
2017, Communications in Nonlinear Science and Numerical SimulationInstability phenomena in impact damper system: From quasi-periodic motion to period-three motion
2017, Journal of Sound and VibrationCitation Excerpt :The smooth and non-smooth bifurcations observed in the vibro-impact oscillators have been widely studied. For smooth bifurcations, Hopf bifurcation [1–7] plays an important part and large progresses have been made in recent years such as researches on the criteria of Hopf bifurcation [8,9], Hopf bifurcation in the resonance points [10], Hopf interaction with period doubling bifurcation [11], anti-controlling of Hopf bifurcation [12,13]. Meanwhile, the non-smooth phenomena such as grazing, chattering and sliding were also investigated theoretically or numerically.
Experimental study of regular and chaotic transients in a non-smooth system
2016, International Journal of Non-Linear MechanicsCitation Excerpt :Dynamical systems exhibiting discontinuous properties have been a rich area of research [1–16], and the range of possible behaviors in the vicinity of bifurcations is carefully described in [17–19].
Torus-doubling bifurcations and strange nonchaotic attractors in a vibro-impact system
2013, Journal of Sound and VibrationCitation Excerpt :Research into the dynamical behaviors of vibro-impact systems has important significance on optimization design of machinery and noise suppression. Early studies on vibro-impact dynamics including the singularities [19–22], global bifurcations [23,24] and routes to chaos [25] have been investigated. In recent years, various bifurcations of vibro-impact systems have received great attention, such as period-doubling bifurcation [26], Hopf bifurcation [27,28] and several types of codimension-2 bifurcations [29–31].
Topology of vibro-impact systems in the neighborhood of grazing
2012, Physica D: Nonlinear Phenomena