Propagating Activity Patterns in Thalamic Neuronal Networks

Singular perturbation methods are used to construct traveling waves for models of thalamic networks. We first study a single layer of mutually inhibitory neurons, each of which has the ability to rebound after hyperpolarization. Two types of waves are constructed: smoothly propagating waves and lurching waves which propagate in a saltatory fashion. We reduce the existence of these waves to simple boundary value problems or algebraic systems which are solved using the computational package AUTO. The resulting calculations are compared to numerical simulations of the network. Finally, some comments are made concerning two-layer networks.