{'fraction_non_alphanumeric': 0.01278772378516624, 'fraction_numerical': 0.0, 'mean_word_length': 5.471074380165289, '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}}
Change in the type of bifurcation resulting in periodic oscillations in delayed feedback diode lasers

The appearance of oscillating regimes in a delayed feedback diode laser is studied analytically and numerically. Based on the Lang—Kobayashi model, the transition of the usual oscillation mechanism, related to the transition through the Hopf bifurcation, to hard excitation of the spike regime is studied. The change in the regime of the instability development has a nature of a phase transition. An explicit expression is derived for the frequency of small harmonic oscillations appearing during the transition through the Andronov—Hopf bifurcation. The boundary between two different regimes of the development of laser power oscillations is determined in the parameter space.