Nonlinear dynamics in breathing-soliton lasers

We review recent advances in the study of nonlinear dynamics in mode-locked fiber lasers operating in the breathing (pulsating) soliton regime. Leveraging advanced diagnostics and control strategies—including genetic algorithms—we uncover a rich spectrum of dynamical behaviours, including frequency-locked breathers, fractal Farey hierarchies, Arnold tongues with anomalous features, and breather molecular complexes. We also identify a novel route to chaos via modulated subharmonic states. These findings underscore the utility of fiber lasers as model systems for exploring complex dissipative dynamics, offering new opportunities for ultrafast laser control and fundamental studies in nonlinear science.