Multi-scale transition network approaches for nonlinear time series analysis

Complex networks are powerful tools for nonlinear time series analysis, which are undergoing fast development in the recent decade. Here we propose a novel way to construct multi-scale transition networks from time series, which are based on coarse-graining partitions of phase space. Using time series from both discrete Hénon map and continuous Rössler systems, we demonstrate that the multi-scale transition entropy values of the resulting networks show the same power as the Lyapunov exponents, identifying chaotic transitions successfully. The advantage is that our method works successfully when only a small number of 3–5 bins is used for the partition generation, while the traditional static node entropy measures work poorly. Further experimental examples in fMRI and ECG analysis show that these entropy measures are able to characterizing different rhythmic states of subjects, showing high potential for time series analysis from complex systems.