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

Time-Delay Identification Using Multiscale Ordinal Quantifiers

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

Ordinal patterns in the Duffing oscillator: Analyzing powers of characterization

Ordinal patterns are a time-series data analysis tool used as a preliminary step to construct the permutation entropy, which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the Lyapunov exponent. However, ordinal patterns store strictly more information than permutation entropy or Lyapunov exponents. We present results working with the Duffing oscillator showing that ordinal patterns reflect changes in dynamical symmetry that is invisible to other measures, even permutation entropy. We find that these changes in symmetry at given parameter values are correlated with a change in stability at neighboring parameters, which suggests a novel predictive capability for this analysis technique.

Exploiting the Nonlinear Dynamics of Optically Injected Semiconductor Lasers for Optical Sensing

Optically injected semiconductor lasers are known to display a rich variety of dynamic behaviours, including the emission of excitable pulses, and of rare giant pulses (often referred to as optical rogue waves). Here, we use a well-known rate equation model to explore the combined effect of excitability and extreme pulse emission, for the detection of variations in the strength of the injected field. We find parameter regions where the laser always responds to a perturbation by emitting an optical pulse whose amplitude is above a pre-defined detection threshold. We characterize the sensing capability of the laser in terms of the amplitude and the duration of the perturbation.

Correlations Preceding High-Intensity Events in the Chaotic Dynamics of a Raman Fiber Laser

We study the time series of the output intensity of a Raman fiber laser with an ordinal patterns analysis in the laminar-turbulent transition. We look for signatures among consecutive events that indicate when the system changes from triggering low-intensity to high-intensity events. We set two thresholds, a low one and a high one, to distinguish between low intensity versus high-intensity events. We find that when the time series is performing low-intensity events (below the low threshold), it shows some preferred temporal patterns before triggering high-intensity events (above a high threshold). The preferred temporal patterns remain the same all through the pump current range studied, even though two clearly different dynamical regimes are covered (laminar regime for low pump currents and turbulent regime for high pump currents). We also find that the turbulent regime shows clearer signatures of determinism than the laminar regime.