Abstract
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.
Highlights
Nature presents many physical systems where the interplay between a deterministic behavior, stochasticity and time delay leads to a broad variety of complex dynamics[1,2,3]
Semiconductor lasers with optical feedback have shown to manifest a wide range of complex dynamics, from periodicity to high dimensional chaos[13]
I) at the onset of the Low Frequency Fluctuations (LFF) regime, and at the transition from the LFF regime to the coherence collapse regime, the dynamics is characterized by two competing behaviors that can be identified with a thresholding method; and ii) in these transition regimes, temporal correlations in the global spiking dynamics can be used to forecast transitions between dynamics, i.e., when the system is performing one
Summary
Nature presents many physical systems where the interplay between a deterministic behavior, stochasticity and time delay leads to a broad variety of complex dynamics[1,2,3]. One particular complex dynamics that semiconductor lasers with feedback can exhibit is the Low Frequency Fluctuations (LFF)[24] In this regime the laser presents an excitable behavior[25], i.e., for perturbations below a threshold the response of the system is linear and of small magnitude, but for perturbations above the threshold the response drives the system to explore a region in phase space far from its stable state, before returning to it. Another relevant system where excitable behavior has been reported are neurons[26], and a lot of research is being done to understand excitability in both systems, and to use semiconductor lasers with feedback to mimic biological neurons[27,28,29,30] This spiking behavior of the laser is consequence of the interplay between nonlinear light-matter interactions, time delay from feedback, and spontaneous emission noise[31]. As we increase the pump current of the laser the LFF dynamics yields to coherence collapse, where the oscillations are too fast and irregular, and the dropouts cannot be distinguished
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