Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy
Zunino, Luciano; Rosso, Osvaldo A.; Soriano, Miguel C.
IEEE Journal of Selected Topics in Quantum Electronics 17, 1250 - 1257 (2011)
The time evolution of the output of a semiconductor laser subject to delayed optical feedback can exhibit high-dimensional chaotic ﬂuctuations. In this contribution, our aim
is to quantify the degree of unpredictability of this hyperchaotic time evolution. To that end, we estimate permutation entropy, a novel information-theory-derived quantiﬁer particularly robust in a noisy environment. The permutation entropy is deﬁned as a functional of a symbolic probability distribution, evaluated using the Bandt–Pompe recipe to assign a probability distribution function to the time series generated by the chaotic system. This measure quantiﬁes the diversity of orderings present in the associated time series. In order to evaluate the performance of this novel quantiﬁer, we compare with the results obtained by using a more standard chaos quantiﬁer, namely the Kolmogorov–Sinai entropy. Here, we present numerical results showing that the permutation entropy, evaluated at speciﬁc time-scales involved in the chaotic regime of the semiconductor laser subject to optical feedback, give valuable information about the degree of unpredictability of the chaotic laser dynamics. The inﬂuence of additive observational noise on the proposed tool is also investigated.