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Method for stabilizing unstable periodic orbits in dynamic-mode atomic force microscopy

Hannes Wallner1,*, Lukas Böttcher2,3, Niklas Kruse1, Wolfram Just1, Ingo Barke2,3, Sylvia Speller2,3, and Jens Starke1

  • *Contact author: hannes.wallner@uni-rostock.de
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Phys. Rev. Applied 25, 044088 – Published 30 April, 2026

DOI: https://doi.org/10.1103/28k1-3tbf

Abstract

We present a noninvasive feedback control scheme to access unstable periodic orbits in dynamic-mode atomic force microscopy. By utilizing this method we are able to explore the complete nonlinear frequency-response curves, including unstable branches between saddle-node bifurcations. The overall scheme is designed to be fast and derivative-free, which allows for simple experimental implementations. The control is closely related to phase-locked loop testing, a truncated Fourier discretization of periodic orbits, and an adaptive filter for online signal demodulation. We demonstrate the feedback control on various contact models for dynamic-mode atomic force microscopy and hope to motivate laboratory experiments by elucidating software and corresponding hardware implementations in detail.

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Phys. Rev. Applied 25, 044088– Published 30 April, 2026
  • Received 8 January 2025
  • Revised 20 February 2026
  • Accepted 11 March 2026
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