Degenerate grazing bifurcations in a three-degree-of-freedom impact oscillator

DOI10.1007/S11071-019-04995-7zbMath1430.34055OpenAlexW2945586822WikidataQ127852992 ScholiaQ127852992MaRDI QIDQ2296971

Jinchen Ji, Shan Yin, Shuning Deng, Gui-Lin Wen

Publication date: 18 February 2020

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-019-04995-7

zbMATH Keywords

Neimark-Sacker bifurcationperturbation of eigenvaluedegenerate grazing bifurcationhigher-order discontinuity mapping

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Bifurcations of singular points in dynamical systems (37G10)

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Cites Work

• Degenerate discontinuity-induced bifurcations in tapping-mode atomic-force microscopy
• Analytical determination for degenerate grazing bifurcation points in the single-degree-of-freedom impact oscillator
• Local analysis of co-dimension-one and co-dimension-two grazing bifurcations in impact micro\-actuators
• Bifurcations of periodic motion in a three-degree-of-freedom vibro-impact system with clearance
• Analysis of chaotic saddles in a nonlinear vibro-impact system
• Use of degeneration to stabilize near grazing periodic motion in impact oscillators
• Numerical analysis of codimension-one, -two and -three bifurcations in a periodically-forced impact oscillator with two discontinuity surfaces
• Bifurcation analysis of an impact oscillator with a one-sided elastic constraint near grazing
• Displayed phenomena in the semi-passive torso-driven biped model under OGY-based control method: birth of a torus bifurcation
• Piecewise-smooth dynamical systems. Theory and applications
• Singularities in soft-impacting systems
• Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model
• Control of near-grazing dynamics and discontinuity-induced bifurcations in piecewise-smooth dynamical systems
• Analytical determination of bifurcations in an impact oscillator
• Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators
• Control of near-grazing dynamics in impact oscillators
• The Effect of Codimension-Two Bifurcations on the Global Dynamics of a Gear Model
• Normal form maps for grazing bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems

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