Critical neuronal models with relaxed timescales separation

TL;DR

This paper explores how relaxing the traditional separation of timescales in neuronal models affects criticality and avalanche statistics, providing new theoretical insights and simulations.

Contribution

It introduces a novel approach to models that partially abandon timescale separation, supported by analytical and numerical analysis.

Findings

Power-law exponents change with increased drive during tasks.

Relaxing timescales alters avalanche statistics.

Analytic and simulation results support the modified models.

Abstract

Power laws in nature are considered to be signatures of complexity. The theory of self-organized criticality (SOC) was proposed to explain their origins. A longstanding principle of SOC is the \emph{separation of timescales} axiom. It dictates that external input is delivered to the system at a much slower rate compared to the timescale of internal dynamics. The statistics of neural avalanches in the brain was demonstrated to follow a power law, indicating closeness to a critical state. Moreover, criticality was shown to be a beneficial state for various computations leading to the hypothesis, that the brain is a SOC system. However, for neuronal systems that are constantly bombarded by incoming signals, separation of timescales assumption is unnatural. Recently it was experimentally demonstrated that a proper correction of the avalanche detection algorithm to account for the increased drive during task performance leads to a change of the power-law exponent from $1.5$ to approximately $1.3$, but there is so far no theoretical explanation for this change. Here we investigate the importance of timescales separation, by partly abandoning it in various models. We achieve it by allowing for external input during the avalanche, without compromising the separation of avalanches. We develop an analytic treatment and provide numerical simulations of a simple neuronal model.