Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In a recent work, mean-field analysis and computer simulations were employed to analyze critical selforganization 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 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.954FAPESP Research, Innovation and Dissemination Center for Neuromathematics [2013/07699-0]CAPES, CNPq, FACEPE, and Centre for Natural and Artifical Information Processing SystemsFAPESP [2016/00430-3, 2016/20945-8]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)