Quantifying complexity of the chaotic regime of a semiconductor laser subject to feedback via information theory measures

Abstract

The time evolution of the output of a semiconductor laser subject to optical feedback can exhibit high-dimensional chaotic fluctuations. In this contribution, our aim is to quantify the complexity of the chaotic time-trace generated by a semiconductor laser subject to delayed optical feedback. To that end, we discuss the properties of two recently introduced complexity measures based on information theory, namely the permutation entropy (PE) and the statistical complexity measure (SCM). The PE and SCM are 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. In order to evaluate the performance of these novel complexity quantifiers, we compare them to a more standard chaos quantifier, namely the Kolmogorov-Sinai entropy. Here, we present numerical results showing that the statistical complexity and the permutation entropy, evaluated at the different time-scales involved in the chaotic regime of the laser subject to optical feedback, give valuable information about the complexity of the laser dynamics.