A General Description of Criticality in Neural Network Models

TL;DR

This paper investigates how criticality emerges in neural network models, identifying key mechanisms and conditions that produce scale-invariant avalanches and diverse firing patterns, with implications for understanding brain dynamics.

Contribution

It introduces a comprehensive analysis of criticality in coupled neural networks, highlighting the roles of synaptic coupling, noise, and bifurcation dynamics in generating critical phenomena.

Findings

Critical avalanches exhibit power-law distributions in specific parameter regimes.

Fast synaptic coupling influences avalanche dynamics mainly in mean-dominated regimes.

The ensemble Kalman filter effectively tracks network connectivity and reproduces critical activity.

Abstract

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A comprehensive study of how criticality emerges and how to reproduce it is still lacking. In this study, we investigate coupled networks with conductance-based neurons and illustrate the co-existence of different spiking patterns, including asynchronous irregular (AI) firing and synchronous regular (SR) state, along with a scale-invariant neuronal avalanche phenomenon (criticality). We show that fast-acting synaptic coupling can evoke neuronal avalanches in the mean-dominated regime but has little effect in the fluctuation-dominated regime. In a narrow region of parameter space, the network exhibits avalanche dynamics with power-law avalanche size and duration distributions. We conclude that three stages which may be responsible for reproducing the synchronized bursting: mean-dominated subthreshold dynamics, fast-initiating a spike event, and time-delayed inhibitory cancellation. Remarkably, we illustrate the mechanisms underlying critical avalanches in the presence of noise, which can be explained as a stochastic crossing state around the Hopf bifurcation under the mean-dominated regime. Moreover, we apply the ensemble Kalman filter to determine and track effective connections for the neuronal network. The method is validated on noisy synthetic BOLD signals and could exactly reproduce the corresponding critical network activity. Our results provide a special perspective to understand and model the criticality, which can be useful for large-scale modeling and computation of brain dynamics.