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

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 or 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 coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

16 pages, 16 figures divided into 7 figures in the article

References in corpus (8)

• Emergent complex neural dynamics
• Dynamical synapses causing self-organized criticality in neural networks
• Criticality in the brain: A synthesis of neurobiology, models and cognition
• Does the 1/f frequency-scaling of brain signals reflect self-organized critical states?
• Self-Organized Criticality model for Brain Plasticity
• Dragon-kings: mechanisms, statistical methods and empirical evidence
• Subsampling scaling: a theory about inference from partly observed systems
• Self-Organization of Dragon Kings

Cited by in corpus (13)

• Self-organization toward criticality by synaptic plasticity
• Feedback mechanisms for self-organization to the edge of a phase transition
• Homeostatic plasticity and external input shape neural network dynamics
• Subsampled directed-percolation models explain scaling relations experimentally observed in the brain
• Synaptic balance due to homeostatically self-organized quasicritical dynamics
• Self-organized critical balanced networks: a unified framework
• Homeostatic Criticality in Neuronal Networks
• Spatial-temporal analysis of neural desynchronization in sleep-like states reveals critical dynamics
• Fractal analyses of networks of integrate-and-fire stochastic spiking neurons
• Coexistence of scale invariant and rhythmic behavior in self-organized criticality
• Physics of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality
• Optimal input reverberation and homeostatic self-organization towards the edge of synchronization
• Less is different: why sparse networks with inhibition differ from complete graphs