Quantifying the irregularity of a time series

We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition network derived from a time series. We demonstrate numerically that circulance sensitively and robustly positions time series of canonical model systems, representative of preset dynamical regimes, along a continuous spectrum from regularity to randomness. Analyzing empirical data from long-term observations of high-dimensional, complex systems—human brain and the Sun—reveals that circulance aids in elucidating different dynamical regimes.