Multistability, relaxation oscillations, and chaos in time-delayed optoelectronic oscillators with direct laser modulation.

We investigate the nonlinear dynamics of an optoelectronic oscillator that is implemented with a laser diode (LD) with time-delayed feedback. In this system, electrical-to-optical conversion is directly implemented using the direct modulation of the laser diode itself, instead of an electrooptical modulator as in conventional architectures. Moreover, we consider the cubic nonlinear saturation of the characteristic laser power-intensity (P-I) transfer function far above threshold, instead of its simplified piecewise linear counterpart. We perform the stability analysis of the oscillator, and we show that it displays a rich dynamics that includes quasi-harmonic, relaxation oscillations, and chaos. We also show that the oscillator is strongly hysteretic and displays a wide variety of multistable behaviors, including the rare case of bistability between chaotic attractors. Our analytical and numerical results are found to be in good agreement with the experimental measurements.

Classification of hyperchaotic, chaotic, and regular signals using single nonlinear node delay-based reservoir computers.

The Lyapunov exponent method is generally used for classifying hyperchaotic, chaotic, and regular dynamics based on the equations modeling the system. However, several systems do not benefit from appropriate modeling underlying their dynamic behaviors. Therefore, having methods for classifying hyperchaotic, chaotic, and regular dynamics using only the observational data generated either by the theoretical or the experimental systems is crucial. In this paper, we use single nonlinear node delay-based reservoir computers to separate hyperchaotic, chaotic, and regular dynamics. We show that their classification capabilities are robust with an accuracy of up to 99.61% and 99.03% using the Mackey-Glass and the optoelectronic oscillator delay-based reservoir computers, respectively. Moreover, we demonstrate that the reservoir computers trained with the two-dimensional Hénon-logistic map can classify the dynamical state of another system (for instance, the two-dimensional sine-logistic modulation map). Our solution extends the state-of-the-art machine learning and deep learning approaches for chaos detection by introducing the detection of hyperchaotic signals.