Estimating Kolmogorov–Sinai entropy from time series of high-dimensional complex systems

A method is presented to estimate KS entropy from time series of a high-dimensional complex system. We focus on partitioned entropy, which measures the complexity of data points localized in a delay-coordinate space. By quantifying the time evolution of the partitioned entropy, we show that its growth rate gives a good estimate of the KS entropy. Our method is computationally efficient, since a time series is discretized into a coarse-grained symbolic sequence by a vector quantization technique. Using numerical data sets generated from prototypical models of chaotic systems, we showed that our approach works quite well for high-dimensional complex systems. Application to experimental data measured from physical models of the vocal membranes confirmed that our method is effective for characterizing the complexity of real-world systems.