{'fraction_non_alphanumeric': 0.015228426395939087, 'fraction_numerical': 0.0, 'mean_word_length': 5.21259842519685, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Numerical analysis of complex dynamics in atomic force microscopes

We model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential, and consider the dynamical behavior of the corresponding harmonically forced system. Existence of chaotic invariant sets predicted by Melnikov theory is then numerically verified. Such dynamics appears to be generated via a cascade of period doubling bifurcations, whose occurrence has been studied as a function of the system parameters. The importance of this analysis is twofold: it can be used to change the AFM operating conditions to a region of the parameter space where regular motion is ensured or it can be useful in designing a controller that stabilizes the system on a non-chaotic trajectory.