An application of Conley index techniques to a model of bursting in excitable membranes

Abstract

Assumptions about a model of bursting activity in pancreatic β-cells are stated and a neighborhood of the attractor in this model is constructed. Conley index results and techniques are used to give a sufficient condition for a singular isolating neighborhood to isolate a nonempty attractor. Finally, this theorem is applied to the bursting model. © 2000 Academic Press.