Synchronization and bifurcation dynamics of dissipative breathing solitons in pure-quartic fiber lasers via external modulation

As a paradigm of nonlinear dynamics, breathing dissipative pure-quartic solitons (DPQSs) have exhibited a variety of unique properties. However, the mechanisms underlying their synchronization and transition to chaos under external modulation remain largely unexplored. Herein, we demonstrate the synchronization dynamics between external modulation signals and breathing DPQSs, as well as the transition dynamics from synchronization to chaos. Our results show that external modulation is not only an effective way to control the breathing frequency, but also a crucial mechanism in the transformation of breathing DPQSs into chaotic solitons. Through analysis of the phase portraits, we confirm that external modulation achieves frequency locking by altering the phase of the original state, and that the breathing intensity is suppressed upon synchronization when the drive frequency approaches the central frequency of the locking range. Moreover, by increasing the drive strength, a novel pathway for the transition of DPQSs from synchronized breathing states to chaotic states has been revealed. These findings provide profound insights into the synchronization mechanisms of nonlinear dynamics and the transition dynamics from synchronized breathing states to chaos in fiber lasers with high-order dispersion.