Composite Poincaré mapping of double grazing in non-smooth dynamical systems: bifurcations and insights

DOI10.1007/S00707-023-03602-6zbMath1526.70021OpenAlexW4381513121MaRDI QIDQ6051227

Yuan Yue, Run Liu

Publication date: 19 September 2023

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

Full work available at URL: https://doi.org/10.1007/s00707-023-03602-6

zbMATH Keywords

local discontinuous mappinglocal normal form mappingmapping singularitynon-classical local bifurcationpiecewise-smooth oscillator

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Normal forms for nonlinear problems in mechanics (70K45)

Cites Work

• Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence: Modelling and experimental verification
• Local analysis of \(C\)-bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems
• Bifurcations of dynamical systems with sliding: derivation of normal-form mappings
• Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts
• Discontinuity-induced bifurcations in a piecewise-smooth capsule system with bidirectional drifts
• Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models
• Calculating the Lyapunov exponents of a piecewise-smooth soft impacting system with a time-delayed feedback controller
• Control of near-grazing dynamics and discontinuity-induced bifurcations in piecewise-smooth dynamical systems
• DETECTION OF GRAZING ORBITS AND INCIDENT BIFURCATIONS OF A FORCED CONTINUOUS, PIECEWISE-LINEAR OSCILLATOR
• Regularization of Planar Piecewise Smooth Systems with a Heteroclinic Loop
• A periodically forced piecewise linear oscillator
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system
• Normal form maps for grazing bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems

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