Noah Parks and Noah Palmer, Department of Applied Mathematics, University of Colorado Boulder

Noah Parks: Perturbation Analysis of a Delay-Coupled Neural Field Model

Noah Palmer: Existence and stability of stationary bumps in an astrocyte-neural field model

Noah Parks: Neural fields are integrodifferential equations used to model neural populations by approximating them as a continuum on some domain. The techniques used to analyze simple forms of these models are well understood. However, little work has been done on the analytical study of neural fields consisting of multiple populations coupled with a fixed-time delay. In this talk, we explore how the aforementioned techniques can be generalized and adapted in order to explore the behavior of solutions in the delayed case. In particular, we wish to determine how localized "bump" solutions evolve when exposed to a small input or translation.

Noah Palmer: Neural field models describe the spatiotemporal evolution of neural activity using integro-differential equations. These models can capture cortical phenomena such as traveling waves, stationary bumps, and spatiotemporal oscillation. However, current formulations typically neglect the role of astrocytes, glial cells that provide metabolic support to neurons, mediate the recycling of neurotransmitters, and modulate synaptic function. In this talk, we introduce an astrocyte-neural field model that incorporates glial feedback into cortical dynamics. We then analyze the existence and stability of stationary bump solutions.