A new approach to uncover dynamic phase coordination and synchronization

Phase attractive maps are an essential mechanism of multi-stable systems such as found in coupled neuronal oscillators, An essential feature of this type of dynamic nonlinear coordination is dynamic phase synchronization. The identification of dynamic phase synchronizations is complicated due to changing frequency ratios of synchronized intervals, other nonstationarities, and noise. In order to overcome these problems the momentary phase relations and their statistics were analyzed by several authors. In this way phase synchronizations also in chaotic and noisy oscillating systems could be uncovered. We propose a novel method which avoids one essential limitation of these approaches, namely the necessity of presetting particular frequency ratios of interest. The proposed novel method was validated by its application to a simulated driven neuronal generator during the transition period between different synchronization modes and to dynamically coupled components of sympathetic nerve discharges.