Assessment of the mutual synchronization of two stochastic data sets: The effects of additive and multiplicative white noise

Joint analysis of complex signals is essential for a better understanding of the principles underlying the complex systems dynamics. In our work we studied the mutual dynamics of two Gaussian distributed stochastic processes exhibiting either short-term or long-term correlations. We generated two copies of each surrogate process and applied the amplitude randomization procedure to one of them. We consider two methods for estimating the stability of their relative dynamics. The first one is based on the calculation of the phase synchronization coefficient Sync and the second one estimates the coefficient of time delay stability TDS between the processes. We found that the TDS does not react to the additive noise, in marked contrast to Sync. Both methods respond to the multiplicative amplitude randomization, but the sensitivity of the method based on the phase synchronization analysis is much higher. We also have shown that both of the coefficients Sync and TDS are more sensitive to the Gaussian noise, compared to the uniformly distributed noise scenario.