Stochastic quorum percolation and noise focusing in neuronal networks

¹ Department de Física de la Matèria condensada, Universitat de Barcelona - E-08028 Barcelona, Spain
² RIKEN Center for Brain Science - Wako-shi, 351-0198 Saitama, Japan
³ Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona E-08028 Barcelona, Spain

Received: 30 October 2020
Accepted: 17 January 2021

Abstract

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