Neural Networks with Dynamical Links and Self-Organized Criticality

João Guilherme Ferreira Campos, Ariadne de Andrade Costa, Mauro Copelli, Osame Kinouchi

In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in excitable cellular automata annealed networks, where randomly chosen links were depressed after each spike. Calculations agree with simulations of the annealed version, showing that the nominal \textit{branching ratio\/} σ converges to unity, and fluctuations vanish in the thermodynamic limit, as expected of a self-organized critical system. However, the question remains whether the same results apply to a biologically more plausible, quenched version, in which the neighborhoods are fixed, and only the active synapses are depressed. We show that simulations of the quenched model yield significant deviations from σ=1, due to spatio-temporal correlations. However, the model is shown to be critical, as the largest eigenvalue λ of the synaptic matrix is shown to approach unity, with fluctuations vanishing in the thermodynamic limit.

The whole paper is available here.

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