Correlations Induced by Depressing Synapses in Critically Self-Organized Networks with Quenched Dynamics

• Published in: arXiv.org
• Main Authors: João Guilherme Ferreira Campos, Ariadne de Andrade Costa, Copelli, Mauro, Kinouchi, Osame
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 20.02.2017
• Subjects: Annealing; Cellular automata; Cellular communication; Computer simulation; Dynamics; Eigenvalues; Physics - Adaptation and Self-Organizing Systems; Quenching; Simulation; Size effects; Synapses; Unity
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1604.05779

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 \textit{branching ratio\/} \(\sigma\) 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 \(\sigma=1\) 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, \(\lambda_c = 1\) . We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.