Reproducing complex explosion and intermittence dynamics in a dissipative soliton laser using a scalar iterative map

Numerical modelling based on purely scalar nonlinear Schrodinger equation propagation is applied to a dissipative soliton laser operating in the soliton-similariton regime and generating parabolic pulses. The model is shown to reproduce a range of instabilities that have been reported in recent experiments. Here, we study in detail the laser stability characteristics as a function of the parameters of the gain medium and the saturable absorber, allowing us to readily identify clear regimes where stable single solitons and soliton molecules are observed. Outside these regimes, we reproduce a wide range of instabilities linked with soliton molecule internal motion, soliton explosions and intermittence.