Assessment of the mutual stability of two correlated stochastic signals: The effects of phase randomization

In complex systems significant information about their inherent dynamics is hidden in the interactions between the system components and thus the analysis of the mutual information is essential for providing a better understanding of the principles underlying the system behavior. We focused on four different methods to assess the mutual information such as phase synchronization analysis; time delay stability estimate; coherence function analysis; cross-conditional entropy estimate. In our work we studied the sensitivity of these methods in relation to the phase randomization. Two classes of normally distributed random short- and long-term correlated stochastic processes were considered. The phase randomization was simulated by adding a uniformly distributed random component to each instantaneous Hilbert phase value. We have shown that the phase synchronization analysis and the cross-conditional entropy estimate are the most sensitive under weak phase detuning conditions. In contrast, the time delay stability estimate and the coherence function analysis are much less sensitive and decay significantly only when the maximum phase deviation is about π/2. Finally, while the phase synchronization analysis depends on the correlation time of the stochastic process studied, the cross-conditional entropy estimate appears invariant to the presence of either short-or long-term correlations in the data.