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Bifurcation and chaos of atomic-force-microscope probes driven in Lennard–Jones potentials

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  • Hu, Qing-Quan
  • Chen, Li-Qun

Abstract

Bifurcation and chaos in atomic force microscope are investigated. The one-term and two-term Galerkin truncations are, respectively, employed to simplify the partial-differential equation that governs the motions of the microcantilever to a set of ordinary differential equations. By use of Poincare maps, the dynamical behaviors are identified based on the numerical solutions of the governing equations. Bifurcation diagrams are presented in the case that the excitation amplitude increases while other parameters are fixed. Numerical simulations indicate that periodic and chaotic motions occur in the system and one-term truncation and two-term truncation give the qualitatively same results.

Suggested Citation

  • Hu, Qing-Quan & Chen, Li-Qun, 2008. "Bifurcation and chaos of atomic-force-microscope probes driven in Lennard–Jones potentials," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 740-745.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:740-745
    DOI: 10.1016/j.chaos.2006.07.004
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    References listed on IDEAS

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    1. Chen, Li-Qun & Chen, Hao & Zu, Jean W., 2006. "Equilibrium and bifurcation of varying cross-section microcantilevers subject to the atomic force," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1159-1164.
    2. Hu, Qing-Quan & Chen, Li-Qun, 2007. "Bifurcation and chaos in atomic force microscope," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 711-715.
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    Cited by:

    1. Chen, Zhenyang & Chen, Fangqi & Wang, Dan & Zhou, Liangqiang, 2021. "Tapping modes in the Atomic Force Microscope model with Lennard-Jones force and slow-fast base motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.

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