Author
Jalics, Jozsi Zoltan

Year
2002

Advisor
Terman, David

Abstract
A variety of experimental and modeling studies have been performed to investigate wave propagation in networks of thalamic neurons and their relationship to spindle sleep rhythms. It is believed that spindle oscillations result from the reciprocal interaction between thalamocortical (TC) and thalamic reticular (RE) neurons. We consider a reduced one-layer network of synaptically coupled, mutually inhibitory TC cells modeled by a system of singularly perturbed integral-differential equations. Geometric singular perturbation methods are used to prove the existence of a locally unique slow wave pulse that propagates along the network. By seeking a slow pulse solution, we are able to reformulate the problem to finding a heteroclinic orbit in a three-dimensional system of ordinary differential equations with two additional constraints on the location of the orbit at two distinct points in time.

Thesis
Jalics.Jozsi.Zoltan.pdf