Degenerate discontinuity-induced bifurcations in tapping-mode atomic-force microscopy

DOI10.1016/j.physd.2009.10.001zbMath1248.37076OpenAlexW2158682041MaRDI QIDQ979086

Mark R. Paul, Sambit Misra, Harry J. Dankowicz

Publication date: 25 June 2010

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2009.10.001

zbMATH Keywords

codimension-two bifurcationsatomic-force microscopybranch point bifurcationdiscontinuity mappingsIsola bifurcationtapping-mode

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

Related Items (13)

A new test for stick-slip limit cycles in dry-friction oscillators with a small nonlinearity in the friction characteristic ⋮ Global detection of detached periodic solution branches of friction-damped mechanical systems ⋮ Complicated periodic cascades arising from double grazing bifurcations in an impact oscillator with two rigid constraints ⋮ New control methodology of microcantilevers in atomic force microscopy ⋮ Analysis of a two-dimensional nonsmooth Poincaré-like map ⋮ Asymptotic analysis of a noncontact AFM microcantilever sensor with external feedback control ⋮ Conditions for the existence of isolated backbone curves ⋮ Nonlinear dynamics and bifurcations in external feedback control of microcantilevers in atomic force microscopy ⋮ Control of near-grazing dynamics and discontinuity-induced bifurcations in piecewise-smooth dynamical systems ⋮ Isolated resonances and nonlinear damping ⋮ Degenerate grazing bifurcations in a three-degree-of-freedom impact oscillator ⋮ Suppression of grazing-induced instability in single degree-of-freedom impact oscillators ⋮ Degenerate Grazing Bifurcations in a Simple Bilinear Oscillator

Cites Work

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• Van der Pol type self-excited micro-cantilever probe of atomic force microscopy
• Singularities and groups in bifurcation theory. Volume I
• Low-velocity impacts of quasiperiodic oscillations.
• On the origin and bifurcations of stick-slip oscillations
• Piecewise-smooth dynamical systems. Theory and applications
• Continuous and discontinuous grazing bifurcations in impacting oscillators
• Controlled onset of low-velocity collisions in a vibro-impacting system with friction
• Nonlinear dynamics as an essential tool for non-destructive characterization of soft nanostructures using tapping-mode atomic force microscopy
• Control of near-grazing dynamics in impact oscillators
• On the stabilizability of near‐grazing dynamics in impact oscillators
• Bifurcations in nonlinear discontinuous systems
• Normal form maps for grazing bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems

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