We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the (bounded) spatial domain consists of two subdomains: a collection of automatic cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.
"Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics." J. Appl. Math. 2009 1 - 17, 2009. https://doi.org/10.1155/2009/292183