Detection Method for Phase Synchronization in a Population of Spiking Neurons

Currently there are many methods to detect synchronization, each of them trying to extract some specific aspects or oriented to specific number or type of signals. In this paper, we present a new method to detect synchronization for multivariate signals, computationally light and not requiring a combinatorial number of operations on signals differences.The method is based on the Hilbert transform of the signals, which provides their instantaneous phases. The distribution of phases for all signals at a specific time is assimilated to a probability distribution. In this way, we obtain a sequence of probability distributions (one per time unit). Computing the entropy of the probability distributions we get finally a function of entropies along time. The average value of this final function provides a good estimate of the synchronization level of the multivariate signals ensemble, and the function itself can be used as a signature (descriptive function) of the whole multidimensional ensemble dynamics.