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

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 \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.

arXiv comment8 pages, 8 figures

References in corpus (11)

• Emergent complex neural dynamics
• Optimal Dynamical Range of Excitable Networks at Criticality
• Dynamical synapses causing self-organized criticality in neural networks
• Self-Organized Criticality model for Brain Plasticity
• Predicting criticality and dynamic range in complex networks: effects of topology
• Approximating the largest eigenvalue of network adjacency matrices
• Self-organization without conservation: true or just apparent scale-invariance?
• Self-organization without conservation: Are neuronal avalanches generically critical?
• Can dynamical synapses produce true self-organized criticality?
• Griffiths phase and long-range correlations in a biologically motivated V1 model
• A solvable non-conservative model of Self-Organized Criticality

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