Susceptibility for extremely low external fluctuations and critical behaviour of Greenberg-Hastings neuronal model

TL;DR

This paper investigates the critical behavior and susceptibility scaling in the Greenberg-Hastings neural model, revealing how spontaneous activation influences phase transitions and exhibits finite size scaling laws.

Contribution

It demonstrates the role of spontaneous activation as an external field and characterizes different activation mechanisms near dynamical phase transitions.

Findings

Susceptibility shows finite size scaling as spontaneous activation tends to zero.

Spontaneous activation acts as an external field related to the order parameter.

Different activation mechanisms are characterized around phase transitions.

Abstract

We consider the scaling behaviour of the fluctuation susceptibility associated with the average activation in the Greenberg-Hastings neural network model and its relation to microscopic spontaneous activation. We found that, as the spontaneous activation probability tends to zero, a clear finite size scaling behaviour in the susceptibility emerges, characterized by critical exponents which follow already known scaling laws. This shows that the spontaneous activation probability plays the role of an external field conjugated to the order parameter of the dynamical activation transition. The roles of different kinds of activation mechanisms around the different dynamical phase transitions exhibited by the model are characterized numerically and using a mean field approximation.