Synchronization in random balanced networks

Luis Carlos Garcidel Molino, Khashayar Pakdaman, Jonathan Touboul, Gilles Wainrib

Published 2013-06-11, updated 2013-10-07Version 3

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states. This transition cannot be explained only through the analysis of the spectral density of the connectivity matrix. We provide a low dimensional approximation that shows the role of both the structure and disorder in the dynamics.