Investigating nonlinear Granger causality method efficiency at strong synchronization of systems

Detecting the direction of coupling between systems using records of their oscillations is an actual task for many areas of knowledge. Its solution can hardly be achieved in case of synchronization. Granger causality method is promising for this task, since it allows to hope for success in the case of partial (e.g., phase) synchronization due to considering not only phases but also amplitudes of both signals. In this paper using the etalon test systems with pronounced time scale the method of nonlinear Granger causality was shown to be effective even in the case of strong phase-locking, with phase synchronization index up to 0.95. Obtained results were tested for significance by various methods based on surrogates times series generation, which showed similar estimates.