Synchronization and Transition Dynamics Between External Modulation and Pulsating Solitons

Pulsation, as an intrinsic second characteristic frequency in nonlinear systems, is highly susceptible to external perturbations. Synchronization phenomena in nonlinear systems, however, offer a robust approach for achieving precise control over pulsation frequencies. In this letter, through experimental studies and numerical simulations performed on a normal-dispersion passively mode-locked erbium-doped fiber laser platform, we demonstrated the synchronization dynamics between an external modulation signal and pulsating solitons including their Arnold tongues and frequency-locking characteristics, while also capturing the transient evolution from asynchronous to synchronous states. Our results show that external modulation synchronization can serve as an effective mechanism for controlling the pulsation frequency. Furthermore, we found that the transition from asynchronous to synchronous behavior primarily originates from phase variations induced by phase synchronization following frequency locking. This phase-driven mechanism provokes drastic energy fluctuations during state transitions, occasionally culminating in temporary pulsation collapse. Numerical simulations further confirmed the synchronization of external modulation and pulsating solitons as well as the transition dynamics, and the slight frequency adjustments induced by synchronization do not significantly perturb the pulsation dynamics. Our work fills a gap in the external modulation-based synchronization control of pulsating soliton frequencies. Besides, our exploration of asynchronous-to-synchronous transitions will inspire investigations into synchronization mechanisms in complex nonlinear systems across various physical domains.