Colloquium

Geometric singular perturbation analysis of neuronal systems

by David Terman,
Professor of Mathematics, Ohio State University, Columbus

Abstract

Models for neuronal systems often exhibit a rich structure ofspatio-temporal activity patterns. In this lecture, I reviewhow such networks are modeled and then discuss the types ofoscillatory and propagating wave-like patterns that may arise.Finally, I demonstrate how methods from geometric singular perturbationtheory have been used to analyze the activity patterns. The analysis isused to study models for scene segmentation and thalamicsleep rhythms.