Forecasting Events in the Complex Dynamics of a Semiconductor Laser with Optical Feedback.

Complex systems performing spiking dynamics are widespread in Nature. They cover from earthquakes, to neurons, variable stars, social networks, or stock markets. Understanding and characterizing their dynamics is relevant in order to detect transitions, or to predict unwanted extreme events. Here we study, under an ordinal patterns analysis, the output intensity of a semiconductor laser with feedback in a regime where it develops a complex spiking behavior. We unveil that, in the transitions towards and from the spiking regime, the complex dynamics presents two competing behaviors that can be distinguished with a thresholding method. Then we use time and intensity correlations to forecast different types of events, and transitions in the dynamics of the system.