Dynamics of Random Networks: Connectivity and First Order Phase Transitions

TL;DR

This paper investigates how increasing connectivity in large random neural networks causes a sudden transition from inactivity to activity, demonstrating a first order phase transition through theoretical and numerical analysis.

Contribution

It reveals that the activity transition in highly diluted random networks is a first order phase transition driven by connectivity.

Findings

Discontinuous jump in network activity at a critical connectivity.

Theoretical and numerical evidence of a first order phase transition.

Connectivity determines the network's transition from inactive to active state.

Abstract

The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the network connectivity the activity changes discontinuously from zero to a finite value as a critical value in the connectivity is reached. Theoretical arguments and extensive numerical simulations indicate that the origin of this discontinuity in the activity of random networks is a first order phase transition from an inactive to an active state as the connectivity of the network is increased.