Capturing synchronization with complexity measure of ordinal pattern transition network constructed by crossplot

To evaluate the synchronization of bivariate time series has been a hot topic, and a number of measures have been proposed. In this work, by introducing the ordinal pattern transition network into the crossplot, a new method for measuring the synchronization of bivariate time series is proposed. After the crossplot been partitioned and coded, the coded partitions are defined as network nodes and a directed weighted network is constructed based on the temporal adjacency of the nodes. The crossplot transition entropy of the network is proposed as an indicator of the synchronization between two time series. To test the characteristics and performance of the method, it is used to analyse the unidirectional coupled Lorentz model and compared it with existing methods. The results showed the new method had the advantages of easy parameter setting, efficiency, robustness, good consistency and suitability for short time series. Finally, electroencephalogram (EEG) data from auditory-evoked potential EEG-biometric dataset are investigated, and some useful and interesting results are obtained.