Stochastic quorum percolation and noise focusing in neuronal networks

Recent experiments have shown that the spontaneous activity of young dissociated neuronal cultures can be described as a process highly inhomogeneous nucleation and front propagation due to localization noise activity, i.e., focusing. However, basic understanding mechanisms build-up leading remain an open fundamental problem. Here we present minimal dynamical model called stochastic quorum percolation account for observed phenomena, while providing robust theoretical framework. The reproduces first second order phase--transitions bursting dynamics avalanches respectively, captures profound effect metric correlations in network topology on dynamics. application our results other systems such infectious diseases rumors is discussed.