Extended detrended cross-correlation analysis of nonstationary processes

We propose an extension of the detrended cross-correlation analysis (DCCA) for signals with highly inhomogeneous structure. The proposed approach evaluates two scaling exponents, one of which characterizes the detrended covariance, and the second exponent quantifies the effects of nonstationarity caused by the distribution of local fluctuations of signal profiles from the trend. Using simulated datasets produced by a system of coupled Lorenz models, we describe entrainment phenomena associated with chaotic synchronization and the role of nonstationarity in their description. The processing of experimental data related to cerebral blood flow in neighboring vessels of different size confirm the general conclusion of this study and shows the possible advantages of the proposed extension of the DCCA-method for diagnosing changes in cooperative dynamics in physiological systems, where the combined effects of dynamics, nonstationarity and noise may occur.