The effects of amplitude randomization on the mutual behaviour of two correlated stochastic signals

The joint analysis of several simultaneously recordered datasets is essential for a better understanding of the principles underlying the complex systems dynamics. Here we consider three methods for the estimation of the stability of the relative dynamics of two processes based on their phase synchronization, coherence function and cross-conditional entropy measures. The first measure is based on the calculation of the phase synchronization coefficient Sync, while the second one is based on the cross-conditional entropy CE. The third approach implies the calculation of the average value of the coherence function of the two processes and is denoted here as the coherence coefficient Coher. All methods were applied to the two types of surrogate normally distributed random stochastic datasets, with either short-term or long-term correlations, characterized by either finite or infinite correlation time, respectively. We created two copies of each dataset and added white noise to one of them with either uniform or Gaussian distribution exhibiting zero mean and equal variance this way simulating the amplitude randomization effect. We next investigated the statistical characteristics of the mutual stability coefficients between the original and the modified datasets. We have shown explicitly that long-term correlations are more vulnerable to the amplitude randomization then short-term correlations. Moreover, coefficients Sync and Coher exhibited different reactions to the increased amplitude randomization for different Hurst exponents, while CE did not show any significant dependence. On the contrary, the influence of the correlation time in short-term correlated datasets could be demonstrated clearly for the coefficients Sync and CE, while no such effect could be observed in Coher. Our results may appear useful in investigations of the mutual dynamics of two datasets in various complex systems analysis including complex networks.