Hopf-flip bifurcation of high-dimensional maps and application to vibro-impact systems

DOI10.1007/s10409-005-0045-7zbMath1200.70025OpenAlexW2042973735MaRDI QIDQ608635

Wangcai Ding, Earl. H. Dowell, Jian-Hua Xie, Lawrence N. Virgin

Publication date: 25 November 2010

Published in: Acta Mechanica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10409-005-0045-7

zbMATH Keywords

mapschaostorusHopf-flip bifurcationvibro-impact dynamics

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55)

Related Items (4)

Extensional channel flow revisited: a dynamical systems perspective ⋮ Discrete-in-time feedback control of near-grazing dynamics in the two-degree-of-freedom vibro-impact system with a clearance ⋮ Vibro-impact dynamics near a strong resonance point ⋮ Analysis of grazing bifurcation from periodic motion to quasi-periodic motion in impact-damper systems

Cites Work

• Hopf bifurcations and chaos of a two-degree-of-freedom vibro-impact system in two strong resonance cases
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Bifurcations de points fixes elliptiques. I: Courbes invariantes
• Quasi-genericity of bifurcations to high dimensional invariant tori for maps
• Bifurcation into invariant tori at points of resonance
• Elements of applied bifurcation theory.
• An experimental impact oscillator
• The dynamics of repeated impacts with a sinusoidally vibrating table
• Nonnormally hyperbolic invariant curves for maps in R³and doubling bifurcation
• Singularities in vibro-impact dynamics
• HOPF BIFURCATION OF A TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM
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