Correlations induced by depressing synapses in critically self-organized networks with quenched dynamics

Physical Review. E
João Guilherme Ferreira CamposO Kinouchi

Abstract

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, λ_{c}=1. We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.

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Citations

Sep 19, 2017·PloS One·Mariana Sacrini Ayres FerrazAlexandre Hiroaki Kihara
Feb 3, 2018·Chaos·Renquan Zhang, Sen Pei
Feb 2, 2021·Frontiers in Neural Circuits·Tawan T A CarvalhoMauro Copelli
Mar 2, 2021·Frontiers in Computational Neuroscience·Kristine HeineyIoanna Sandvig
Aug 21, 2021·Physical Review. E·Renata PazziniAriadne A Costa

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