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.
Highlights
Neuronal network models are extended dynamical systems that may present different collective behaviors or phases characterized by order parameters
In Brochini et al [28], we proposed a new self-organization mechanism based on dynamic neuronal gains Γi [t] while keeping the synapses Wij fixed [28]
We have shown in this paper that dynamic neuronal gains lead naturally to self-organized supercriticality (SOSC) and not self-organized critical (SOC)
Summary
Neuronal network models are extended dynamical systems that may present different collective behaviors or phases characterized by order parameters. The separation regions between phases can be described as bifurcations in the order parameters or phase transitions. In several models of neuronal activity, the relevant phase change is a continuous transition from an absorbing silent state to an active state [1,2,3]. In such a continuous transition, we have a critical point (in general, a critical surface) where concepts of universality classes and critical exponents (among others) are valid. Since the landmark findings of Beggs and Plenz in 2003 [2], these behaviors have been reported in biological networks; see the reviews [4,5,6,7]
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