Detecting coupling directions in multivariate oscillatory systems

Determination of synchronization phenomena between pairs of coupled multivariate processes is of particular interest in Nonlinear Dynamics. Besides synchronization phenomena, coupling directions between the processes are investigated. We present an approach to analyze coupling directions in multivariate oscillatory stochastic systems. We propose usage of partial directed coherence developed in the framework of linear stochastic processes. We show that partial directed coherence is also applicable to detect coupling directions in nonlinear systems such as coupled stochastic van der Pol and stochastic Rossler systems. Furthermore, a differentiation between direct and indirect couplings in multivariate systems is possible when applying partial directed coherence.