2016/04/30 by João G. F. Campos, João Guilherme Ferreira Campos, Ariadne de Andrade Costa +2 · 2 citations
Engineering · Mathematics · Neuroscience · Physics and Astronomy · #Advanced Memory and Neural Computing #Algorithm #Cellular automaton #Eigenvalues and eigenvectors #Lambda #Limit (mathematics) #Mathematical analysis #Mathematics #Mean field theory #Neural dynamics and brain function #Physics #Quantum mechanics #Sigma #Statistical physics #Thermodynamic limit #Thermodynamics #Work (physics) #nlin.AO #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.95.042303
published as Phys. Rev. E 95, 042303 (2017) · 8 pages, 8 figures
arxiv created 2017/02/20 · openalex publication_date 2017/04/10 · arxiv updated 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the so-called annealed dynamics). Calculations agree with simulations of the annealed version, showing that the nominal branching ratio σ converges to unity in the thermodynamic limit, as expected of a self-organized critical system. However, the question remains whether the same results apply to the biological case where only the synapses of firing neurons are depressed (the so-called quenched dynamics). We show that simulations of the quenched model yield significant deviations from σ=1 due to spatial correlations. However, the model is shown to be critical, as the largest eigenvalue of the synaptic matrix approaches unity in the thermodynamic limit, that is, λc=1. We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.