Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record.We study the problem of initiation of propagation of excitation waves in the FitzHugh-Nagumo model. Our approach is based on earlier works, based on the idea of approximating of the boundary between basins of attraction of propagating wave solutions and of decaying solutions as the stable manifold of the 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.VNB gratefully acknowledges the current financial support of the EPSRC via grant EP/N014391/1 (UK