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Velocity of pulses in discrete excitable systems. (English) Zbl 1253.35114

Summary: The pulse solution of the spatially discrete excitable FitzHugh-Nagumo (FHN) system is approximately constructed using matched asymptotic expansions in the limit of large time scale separation (as measured by a small dimensionless parameter \(\epsilon \)). The pulse profile typically consists of slowly varying regions of the excitatory variable separated by sharp wave fronts. In the FHN system, the velocity of a pulse is decided by the interaction between its leading and trailing fronts, but the leading order approximation gives only a fair result when compared with direct numerical solutions. A higher order approximation to the wave fronts comprising the FHN pulse is found. Our approximation provides an \(\epsilon \)-dependent pulse velocity that approximates much better the velocity obtained from numerical solutions. As a result, the reconstruction of the FHN pulse using the improved wave fronts is much closer to the numerically obtained pulse.

MSC:

35Q35 PDEs in connection with fluid mechanics
35C20 Asymptotic expansions of solutions to PDEs
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