{'fraction_non_alphanumeric': 0.018255578093306288, 'fraction_numerical': 0.0, 'mean_word_length': 5.098765432098766, '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}}
Direct Lyapunov method in the theory of replicator system with entropy-like applications

In this report I summarize the results in the application of Direct Lyapunov method to the classical and generalized replicator systems. Based on this results it is shown that there are exist two types of Lyapunov functions: fitness-like and entropy-like. As example it'll be establish that practically all known entropy measures may be obtain from entropy-like Lyapunov function for replicator systems.