Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson–Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson–Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures.Electronic Supplementary MaterialThe online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

This paper contains an analysis of a simple neural network that exhibits self-organized criticality. Such criticality follows from the combination of a simple neural network with an excitatory feedback loop that generates bistability, in combination with an anti-Hebbian synapse in its input pathway. Using the methods of statistical field theory, we show how one can formulate the stochastic dynamics of such a network as the action of a path integral, which we then investigate using renormalization group methods. The results indicate that the network exhibits hysteresis in switching back and forward between its two stable states, each of which loses its stability at a saddle-node bifurcation. The renormalization group analysis shows that the fluctuations in the neighborhood of such bifurcations have the signature of directed percolation. Thus the network states undergo the neural analog of a phase transition in the universality class of directed percolation. The network replicates precisely the behavior of the original sand-pile model of Bak, Tang & Wiesenfeld.arXiv:1209.3829v1 [q-bio.NC] 18 Sep 2012Self-organized criticality in a neural network

No abstract

No abstract