Global synchronization due to cluster size heterogeneity in balanced neural networks

Synchronized brain rhythms have been associated with various cognitive functions as well as neurological disorders, and comprehending how the network connectivities give rise to these behaviors is essential for a better understanding of the importance of network topology on functional brain dynamics. Previous studies have shown that cortical networks with clustered connections give rise to correlated dynamics in individual clusters. However, this same model applied to a network with highly heterogeneous cluster sizes leads to a clear breakdown of the balanced state. In this talk, using a formal definition of the balance matrix, we show why the balance condition breaks and propose a solution to restore balance in the heterogeneous networks. In doing so, we also observe that global synchronization in firing dynamics appears due to cluster size heterogeneity. This modified balance matrix applied to a homogeneous network results in the disappearance of the synchronization. Diversity in cluster sizes has not previously been shown to produce such a global effect in a network of excitatory and inhibitory leaky integrate and fire neurons, and may have important implications in real world cortical networks.