Bifurcations, basin erosion and dynamic integrity in a single-mode model of noncontact atomic force microscopy

Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma “La Sapienza”, 00197 Rome, Italy

Abstract

The nonlinear dynamical behavior of a single-mode model of noncontact AFM is analyzed in terms of attractors robustness and basin integrity. The model considered for the analyses, proposed by Hornstein and Gottlieb [7], consistently includes the nonlinear atomic interaction and the scan control, which appears as parametric excitation. Local bifurcation analyses are carried out to define the overall stability boundary in the excitation parameter space as the envelope of system local escapes, to be compared with the one obtained via numerical simulations. The dynamical integrity of the periodic bounded solutions is studied, and basin erosion is evaluated by means of IF and GIM integrity measures. The obtained erosion profiles allow us to dwell on the possible lack of homogeneous safeness of the stability boundary in terms of attractors robustness and to identify practical escape thresholds ensuring an a priori design safety target.