Synchronization in random balanced networks.

Laboratoire Analyse Geometrie et Applications, University Paris 13, France(Dated: January 10, 2014)Characterizing the inuence of network properties on the global emerging behavior of interactingelements constitutes a central question in many areas, from physical to social sciences. In this articlewe study a primary model of disordered neuronal networks with excitatory-inhibitory structure andbalance constraints. We show how the interplay between structure and disorder in the connectivityleads to a universal transition from trivial to synchronized stationary or periodic states. Thistransition cannot be explained only through the analysis of the spectral density of the connectivitymatrix. We provide a low dimensional approximation that shows the role of both the structure anddisorder in the dynamics.