Statistical analysis of a Potts glass model of cortical dynamics

Abstract

We introduce, in a previously studied Potts model of long-range cortical interactions, a differentiation between a frontal and a posterior subnetwork. "Frontal" units, representing patches of anterior cortex, are endowed with a higher number S of attractor states, in keeping with the larger number of local synaptic contacts of neurons there, than in occipital cortex. A thermodynamic analysis and computer simulations confirm that disorder leads to glassy properties and slow dynamics but, surprisingly, the frontal network, which would be slower if isolated, becomes faster than the posterior network when interacting with it. From an abstract, drastically simplified model we take some steps towards approaching a neurally plausible one, and find that the speed inversion effect is basically preserved.