Emergence of Scale-free Graphs in Dynamical Spiking Neural Networks

In this paper we discuss the presence of a scale-free property in spiking neural networks. Although as argued in the papers by Amaral et al. (2000) and Koch and Laurent (1999), some biological neural networks do not reveal scale-free nature on the level of single neurons, we believe, based on previous research (Piekniewski and Schreiber, 2007) and numerical simulations presented in this article, that such structures should emerge on the level of neuronal groups as a consequence of their rich dynamics and memory properties. The network we analyze is built upon the spiking model introduced by Eugene Izhikevich (2003; 2006). It is formed as a set of randomly constructed neuronal groups (each group to some extent resembles the original model), connected with Gaussian weights. Such a system exhibits rich dynamics, with chattering, bursting and other forms of neuronal activity, as well as global synchronization episodes. We analyze similarities of spike trains of neurons coming from different groups, and build a weighted graph which approximates the similarity of activities (synchronization) of pairs of units. The output graph reveals a scale-free structure giving support to our claim.