A novel and effective method to characterize complex systems

Box-counting dimension and dispersion entropy dynamic plane (BCDDE) is introduced for quantifying complex behavior of dynamical systems. This measurement integrates the advantages of two essential mathematical tools. We undertake the experiment to support the hypothesis of BCDDE. Numerical simu-lations and analysis are performed to prove the effectiveness of the method. The produced results verify that the BCDDE not only can exactly describe the dynamic characteristics of time series, but also can dis-tinguish different classes of time series. The empirical research on the financial time series mainly studies the classification for stock market dynamics. The experimental results are statistically significant, which illustrate that BCDDE can effectively detect the internal structure of the stock market. It turns out that the classification accuracy is excellent between developed stock indices and emerging stock indices. (c) 2021 Elsevier Ltd. All rights reserved.