Abstract
This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion coefficients in which RW solutions are observed will be described using bifurcation theory and continuation methods. The bifurcation of time-periodic solutions of these FHN equations without diffusion is described first. Similar methods are then used to find RW solutions on a circular ring and numerical simulations are described. These results are then extended to investigate RW solutions on annular rings of finite cross-section. Scaling arguments are used to show how the existence of solutions depends on either the diffusion coefficient or on the size of the region.
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Alford, J.G., Auchmuty, G. Rotating wave solutions of the FitzHugh–Nagumo equations. J. Math. Biol. 53, 797–819 (2006). https://doi.org/10.1007/s00285-006-0022-1
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DOI: https://doi.org/10.1007/s00285-006-0022-1