Predicting chaotic time series using optoelectronic feedback laser
Résumé
We study delay-based photonic reservoir computing using a semiconductor laser with an optoelectronic feedback. A rate-equation model for a laser with an optoelectronic filtered feedback is used. The filter allows only highfrequency signals to pass through the feedback loop. The delay-differential equation model consists of three equations for the normalized electric field intensity, the carrier density, and the filtered intensity signal. The stability boundaries which correspond to the Hopf bifurcation condition are determined analytically, showing multiple Hopf bifurcation branches in the dynamics, and the parity asymmetry with relation to the feedback sign. We use the Santa Fe time-series prediction task to evaluate the performance of reservoir computing. Our objective is to determine location of the optimal operating point defined as corresponding to minimal normalized mean square error (NMSE) and relate it to the stability properties of the system. We use 3000 points for training and 1000 for testing; the number of virtual nodes is chosen in regard to the relaxation oscillation frequency. The input signal is determined by the chaotic waveform having n sampling points, and three cases are investigated prediction of n + 1, n + 2 or n + 3 sampling point. The minimum values of NMSE for the n + 2 and n + 3 point prediction tasks correspond to the Hopf bifurcation, and only for the positive feedback.
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