{'fraction_non_alphanumeric': 0.013100436681222707, 'fraction_numerical': 0.0, 'mean_word_length': 5.557142857142857, '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}}
The transcritical bifurcation in absolutely stable feedback systems

The paper gives new conditions for the occurrence of a transcritical bifurcation in a non-negative passive system under non-linear static feedback. In biological systems, this provides a mechanism for defining activation thresholds in positive feedback systems. We apply the results to a simple gene regulation system to compute an activation threshold in the feedback regulation strength.