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Entropy 2017, 19(8), 399; https://doi.org/10.3390/e19080399

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

1
Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405, USA
2
Instituto de Computação, Universidade de Campinas, Campinas-SP 13083-852, Brazil
3
Departamento de Estatística, Instituto de Matemática e Estatística (IME), Universidade de São Paulo, São Paulo-SP 05508-090, Brazil
4
Departamento de Física, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP), Universidade de São Paulo, Ribeirão Preto-SP 14040-901, Brazil
*
Author to whom correspondence should be addressed.
Received: 23 May 2017 / Revised: 27 July 2017 / Accepted: 31 July 2017 / Published: 2 August 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
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Abstract

Networks of stochastic spiking neurons are interesting models in the area of theoretical neuroscience, presenting both continuous and discontinuous phase transitions. Here, we study fully-connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality (SOSC)) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and Dragon-king avalanches. We also find that neuronal gains can produce collective oscillations that coexist with neuronal avalanches. View Full-Text
Keywords: self-organized criticality; neuronal avalanche; stochastic neuron; spiking neuron; neuron models; neuronal networks; power law; supercriticality self-organized criticality; neuronal avalanche; stochastic neuron; spiking neuron; neuron models; neuronal networks; power law; supercriticality
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Costa, A.A.; Brochini, L.; Kinouchi, O. Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons. Entropy 2017, 19, 399.

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