Quantifying the nonlinear complexity of optical time-delayed chaotic systems based on reservoir computing

In this work, we propose a method for measuring the dynamical complexity of optical time-delayed (TD) chaotic systems. The mapping relationship between the system output and its time delay variant is learned by the reservoir computing (RC) network. The learning performance of RC networks can reflect the difficulty of the system's dynamics reconstruction and is quantified as a metric to measure the system complexity. For the well-known two kinds of optical TD chaotic generators, our metric appears more responsive to changes in system parameters compared to permutation entropy (i.e., a premier indicator used for complexity of optical chaotic time series), fractal dimension, and maximal Lyapunov exponent. We also study the relationship between the complexity metric and the time delay signature of optical TD chaotic systems. The results indicate that there is an inverse relationship between them over a wide range of parameters. We believe that this work can provide ideas for security evaluation of an optical chaotic generator from the perspective of underlying dynamics reconstruction.