A numerical and analytical study was conducted to investigate the bifurcation mechanisms that cause desynchronization between the soliton repetition frequency and the frequency of external pulsed injection in a Kerr cavity described by the Lugiato-Lefever equation (LLE). The results suggest that desynchronization typically occurs through an Andronov-Hopf (AH) bifurcation. Additionally, a simple and intuitive criterion for this bifurcation to occur is proposed.
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