Synchronous Neural Activity in Scale-Free vs. Random Network Models

Synchronous firing peaks, at levels greatly exceeding background activity, have recently been reported in neocortical tissue. A small subset of neurons is dominant in a large fraction of the peaks. This has been related to the elevated .ring rate of neurons in the depolarized ‘UP’ state. We report numerical and analytic studies of network behavior in which the network is either random (Erdos-Renyi) or has a power-law (‘scale-free’) node degree distribution. The latter type of network has been widely found in a variety of biological, computer, and social networks. Using a simple, modified Hopfield-type, dynamical rule to generate the time course of firing activity, we find that scale-free networks typically generate extremely large synchronous firing peaks in which a small subset of active nodes is dominant, while random networks do not. This suggests that network topology may play an important role in determining the nature and magnitude of synchronous neural activity.