Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots

Abstract

We present a method for synchronization analysis, that is able to handle large networks of interacting dynamical units. We focus on large networks with different topologies (random, small-world and scale-free) and neuronal dynamics at each node. We consider neurons that exhibit dynamics on two time scales, namely spiking and bursting behavior. The proposed method is able to distinguish between synchronization of spikes and synchronization of bursts, so that we analyze the synchronization of each time scale separately. We find for all network topologies that the synchronization of the bursts sets in for smaller coupling strengths than the synchronization of the spikes. Furthermore, we obtain an interesting behavior for the synchronization of the spikes dependent on the coupling strength: for small values of the coupling, the synchronization of the spikes increases, but for intermediate values of the coupling, the synchronization index of the spikes decreases. For larger values of the coupling strength, the synchronization index increases again until all the spikes synchronize.