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Extraction of nonlinear dynamics for laser diodes with feedback in chaotic regime

It is shown that the nonlinear dynamics of semiconductor lasers with electro-optical feedback can be reconstructed using a new type of neural network with two modules: one for non-feedback part with input data delayed by the embedding time, and a second one for the feedback part with input data delayed by the feedback time. The delay time is obtained by using a simple method based on the forecast error of a linear model. Two values of the feedback strength have been considered that yield nonlinear feedback functions with 1 and 3 extremes. We have found that the complexity of the neural network model required to reconstruct nonlinear dynamics increases with the feedback strength, but not with the delay time. Therefore, the confidentiality level of systems with electro-optical feedback increases with the feedback strength. Chaos synchronization of the simulation data with data obtained from the approximated neural system is obtained when both systems are coupled in a diffusive way. Synchronization with the neural network model is used to extract by substraction a message added to the chaotic carrier.