An application of Conley index techniques to a model of bursting in excitable membranes (Q1566848)

A singular perturbation problem for the parameterized system of equations \[ \dot x=f_0(x)+\epsilon f_1(x) \] is considered. Let \(N\) be a singular isolating neighborhood of the system. The main result of the paper provides a sufficient condition under which the invariant part of \(N\) is an attractor for \(\epsilon >0\) small enough. The result is applied to prove the existence of an attractor for a system based on a model of electrical activity of pancreatic \(\beta\)-cells.