Soliton as strange attractor: nonlinear synchronization and chaos

We show that dissipative solitons can have dynamics similar to that of a strange attractor in low-dimensional systems. Using a model of a passively mode-locked fiber laser as an example, we show that soliton pulsations with periods equal to several round-trips of the cavity can be chaotic, even though they are synchronized with the round-trip time. The chaotic part of this motion is quantified using a two-dimensional map and estimating the Lyapunov exponent. We found a specific route to chaotic motion that occurs through the creation, increase, and overlap of "islands" of chaos rather than through multiplication of frequencies.