Inferring Asymmetric Relations between Interacting Neuronal Oscillators

We apply a quantitative method for the identification of asymmetric relations between weakly interacting self-sustained oscillators to the study of rhythmic neural electrical activ- ity. We begin by testing the method on biophysically motivated neural oscillator models considering first two diffusively coupled Hindmarsh-Rose oscillators, and then two ensembles of globally coupled neurons interacting through their mean fields. Next, we consider the more complex case of interactions among several oscillatory units. The method is further applied to the analysis of the control of externally vs internally paced movements in humans. A pilot study in one healthy subject reveals that asymmetry of interactions between different brain areas may strongly change with the transition from external to internal pacing, while the degree of synchronization hardly changes. Furthermore, our preliminary results highlight the important role of the secondary auditory cortex in internal rhythm generation.