Chaos Identification Based on Component Reordering and Visibility Graph

The identification between chaotic systems and stochastic processes is not easy since they have numerous similarities. In this study, we propose a novel approach to distinguish between chaotic systems and stochastic processes based on the component reordering procedure and the visibility graph algorithm. It is found that time series and their reordered components will show diverse characteristics in the 'visibility domain'. For chaotic series, there are huge differences between the degree distribution obtained from the original series and that obtained from the corresponding reordered component. For correlated stochastic series, there are only small differences between the two degree distributions. For uncorrelated stochastic series, there are slight differences between them. Based on this discovery, the well-known Kullback–Leible divergence is used to quantify the difference between the two degree distributions and to distinguish between chaotic systems, correlated and uncorrelated stochastic processes. Moreover, one chaotic map, three chaotic systems and three different stochastic processes are utilized to illustrate the feasibility and effectiveness of the proposed method. Numerical results show that the proposed method is not only effective to distinguish between chaotic systems, correlated and uncorrelated stochastic processes, but also easy to operate.