Homeostatic Criticality in Neuronal Networks

TL;DR

This paper introduces homeostatic mechanisms in neuronal networks that enable self-organized quasi-criticality, maintaining near-critical behavior despite external inputs, thus addressing limitations of traditional criticality models.

Contribution

It proposes simple homeostatic rules for neuronal networks that sustain near-critical states under external input, expanding understanding of self-organization in complex systems.

Findings

Homeostatic mechanisms promote self-organization of network parameters.

Near criticality is achievable with proper timescale separation.

Mechanisms may apply to other complex systems like earthquakes and epidemics.

Abstract

In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing external fields $h \to 0$. Considering that this is rarely the case for natural systems, such a restriction poses a challenge to the explanatory power of these models. Besides that, in models of dissipative systems like earthquakes, forest fires, and neuronal networks, there is no true critical behavior, as expressed in clean power laws obeying finite-size scaling, but a scenario called "dirty" criticality or self-organized quasi-criticality (SOqC). Here, we propose simple homeostatic mechanisms which promote self-organization of coupling strengths, gains, and firing thresholds in neuronal networks. We show that with an adequate separation of the timescales for the coupling strength and firing threshold dynamics, near criticality (SOqC) can be reached and sustained even in the presence of significant external input. The firing thresholds adapt to and cancel the inputs ($h$ decreases towards zero). Similar mechanisms can be proposed for the couplings and local thresholds in spin systems and cellular automata, which could lead to applications in earthquake, forest fire, stellar flare, voting, and epidemic modeling.