Colloquium

Neuronal Dynamics

by David Terman, Professor, Ohio State University, Columbus

Abstract

Oscillations and other patterns of neuronal activity arise throughoutthe central nervous system. This activity has been observed in sensoryprocessing, motor activities, and learning, and has been implicated inthe generation of sleep rhythms, epilepsy, and parkinsonian tremor.Mathematical models for neuronal activity often display an incrediblyrich structure of dynamic behavior. In this lecture, I describe how theneuronal systems can be modeled, various types of activity patterns thatarise in these models, and mechanisms for how the activity patterns aregenerated. In particular, I demonstrate how methods from geometricsingular perturbation theory have been used to analyze propagating wave-likeactivity patterns in excitatory-inhibitory neuronal systems.