{'fraction_non_alphanumeric': 0.01616161616161616, 'fraction_numerical': 0.0, 'mean_word_length': 5.985915492957746, '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}}
Vibrational control of nonlinear systems

The purpose of this paper is to establish the basis of vibrational control theory for nonlinear systems. The notions of vibrational stabilizability and vibrational controllability of nonlinear finite-dimensional systems are introduced and analyzed. Calculation formulae are derived. Transient behavior of vibrationally controlled nonlinear systems is studied. Several examples, including forced Duffing, Rayleigh and Van der Pol equations are discussed.