Study of power-law activity distributions in a spiking neural network model

¹ School of Biopharmaceutical and Medical Sciences, Sungshin Women's University - Seoul 01133, Korea
² Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University Seoul 08826, Korea

^(a) E-mail: mychoi@snu.ac.kr (corresponding author)

Received: 13 March 2023
Accepted: 27 July 2023

Abstract

Neuronal avalanches are cascades of bursts of activity observed primarily in the superficial cortical layers, the distribution of which fits a power law well. Motivated by the observation, we study how a power-law activity distribution emerges in a spiking neural network model. Specifically, we clarify the fundamentals of the phenomenon by applying a general theory of scale-free behavior, introduced to explain the power-law degree distribution in a brain network, and disclose that two kinds of fluctuations in spiking dynamics serve as the essential mechanism for the phenomenon. It is shown that the scale-free behavior arises from a Markov process or a Fokker-Planck diffusion in one dimension and how the power-law exponent of the activity distribution is determined depending on several factors, including the time bin. Finally, we also explain the scale-free behavior observed in the statistics of activity lifetimes.