{'fraction_non_alphanumeric': 0.020604395604395604, 'fraction_numerical': 0.01098901098901099, 'mean_word_length': 5.5675675675675675, '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}}
Japanese Contributions to Nonlinear Cycle Theory in the 1950s

In the early 1950s pioneering contributions were made to the nonlinear theory of Keynesian macrodynamics by Shinichi Ichimura, Michio Morishima and Takuma Yasui. They were the first to formally investigate the existence, stability and uniqueness of limit cycles in macrodynamics. An attempt is made to place the contributions of this Japanese school of nonlinear trade cycle theorists within the context and development of math‐ematical economics in early post‐war Japan. As an additional, although minor, exercise, Morishima's model of the cycle is simplified and generalized to show, using the Andronov‐Hopf bifurcation theorem, the existence of a periodic orbit.