Control of excitable systems is optimal near criticality

TL;DR

This paper investigates how controlling neural activity near criticality can mitigate noise, showing that control is most effective close to critical points despite the inherent noisiness of this regime.

Contribution

It provides a combined numerical and analytical analysis of control efficacy in neural networks near criticality, highlighting optimal control conditions.

Findings

Control is most effective near criticality.

Optimal control slightly away from criticality in heterogeneous networks.

Criticality offers a balance between noise and controllability.

Abstract

Experiments suggest that cerebral cortex gains several functional advantages by operating in a dynamical regime near the critical point of a phase transition. However, a long-standing criticism of this hypothesis is that critical dynamics are rather noisy, which might be detrimental to aspects of brain function that require precision. If the cortex does operate near criticality, how might it mitigate the noisy fluctuations? One possibility is that other parts of the brain may act to control the fluctuations and reduce cortical noise. To better understand this possibility, here we numerically and analytically study a network of binary neurons. We determine how efficacy of controlling the population firing rate depends on proximity to criticality as well as different structural properties of the network. We found that control is most effective - errors are minimal for the widest range of target firing rates - near criticality. Optimal control is slightly away from criticality for networks with heterogeneous degree distributions. Thus, while criticality is the noisiest dynamical regime, it is also the regime that is easiest to control, which may offer a way to mitigate the noise.