Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics

Figure 1

Spreading of the wave. The automatic domain is located on [−1,1] and the FitzHugh-Nagumo parameters 𝜖=0.05 and 𝛾=0.5 are used. Depicted are the function 𝜉 in (2.6) (giving the spatial shape of the approximative solution (3.28)) and the automaticity function in (2.2) for different values of 𝛼 and 𝛽. The corresponding critical diffusion coefficient 𝜂₀ and the values of 𝑘=(𝛼/𝜖−𝛾)/𝜂₀ and 𝜅=(𝛽/𝜖+𝛾)/𝜂₀ in the function 𝜉 are indicated as well. Upper row: increasing automaticity 𝛼 of the automatic cells makes the wave spread further into the surrounding tissue. Lower row: decreasing stability 𝛽 of the normal cells makes the wave spread further into the surrounding tissue.

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