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Updated: Feb 22, 2026

Reaction Kinetics and Combustion Dynamics of I4O9 and Aluminum Mixtures
Published on: November 7, 2016
Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
1College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom.
Abstract:
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.
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