Existence and Stability of Standing Spot Solutions in a Three-Component FitzHugh-Nagumo System in R2

This manuscript presents a mathematically rigorous proof for the location of eigenvalues of a linearized eigenvalue problem regarding standing spot solutions in a three-component FitzHugh-Nagumo system in R2 using an analytical singular perturbation technique. This result was already provided by [P. van Heijster and B. Sandstede, Phys. D, 275 (2014), pp. 19--34] by formal asymptotic analysis, in which they showed that stable traveling spot solutions bifurcate from stable standing ones via a drift bifurcation by combining analytical and numerical methods. Moreover, our result simultaneously provides approximations of eigenfunctions corresponding to the eigenvalues.