Complexity and information measures in planar characterization of chaos and noise

In this work, we present a comprehensive assessment of the Fisher information measure and statistical complexity measures based on Euclidean distance, Wootters distance and Jensen–Shannon divergence, regarding their abilities to (planar-) distinguish between/among (1) chaos and periodicity; (2) different degrees of periodicities; (3) different chaotic regimes; and (4) chaos and noise, and characterize delay dynamics. The Bandt–Pompe approach is used to build up the probability space to generate the entropy-complexity/information plane. The effect of embedding parameters on the evaluation is also considered. Within this framework, complexity measures based on the Wootters distance and Jensen–Shannon divergence are superior to the Fisher information measure in capturing subtle details of chaotic dynamics. The Fisher information measure shows advantages in robustness to additive noises and in planar-behavior representation of chaos and noise. Moreover, all measures are able to properly characterize the intrinsic delay dynamics of chaotic and stochastic systems. Nevertheless, the complexity measure based on the Euclidean distance is not valid by definition, thus, not applicable at any cases.