Predicting critical ignition in slow-fast excitable models

Understand

Linearization around unstable travelling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family of spatially confined perturbations to the rest state.

• This theory relies on the knowledge of the unstable travelling wave solution as well as the leading left and right eigenfunctions of its linearization.
• We investigate the asymptotics of these ingredients, and utility of the resulting approximations of the strength-extent curves, in the slow-fast limit in two-component excitable systems of FitzHugh-Nagumo type, and test those on four illustrative models.
• Of these, two are with degenerate dependence of the fast kinetic on the slow variable, a feature which is motivated by a particular model found in the literature.