{'fraction_non_alphanumeric': 0.024439918533604887, 'fraction_numerical': 0.008146639511201629, 'mean_word_length': 5.0, '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}}
Painlevé analysis and exact solutions of a predator–prey system with diffusion

A system of equations for description of the predator–prey relations is considered. The model corresponds to the modified Lotka–Volterra system with logistic growth of the prey and with both predator and prey dispersing by diffusion. The Painlevé analysis of the system of equations is studied. Exact traveling wave solutions are found by means of the Q‐function method. Copyright © 2014 John Wiley & Sons, Ltd.