Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions.

We model the dynamical behavior of the neuropil, the densely interconnected neural tissue in the cortex, using neuropercolation approach. Neuropercolation generalizes phase transitions modeled by percolation theory of random graphs, motivated by properties of neurons and neural populations. The generalization includes (1) a noisy component in the percolation rule, (2) a novel depression function in addition to the usual arousal function, (3) non-local interactions among nodes arranged on a multi-dimensional lattice. This paper investigates the role of non-local (axonal) connections in generating and modulating phase transitions of collective activity in the neuropil. We derived a relationship between critical values of the noise level and non-locality parameter to control the onset of phase transitions. Finally, we propose a potential interpretation of ontogenetic development of the neuropil maintaining a dynamical state at the edge of criticality.