Measuring the degree of synchronization from time series data

Abstract
A novel approach is presented to measure the synchronization of two time series. Based on the consistent changing tendency of temporal permutation entropies, we introduce an order parameter to characterize the synchronization between two coupled systems. The value of the order parameter can be used as an indicator of the degree of synchronization, which has been confirmed by numerical simulations and analytically illustrated through an example. Our method is effective and can be easily used in practical situations.