Pinned solutions in a heterogeneous three-component FitzHugh-Nagumo model (Q1739077)

This article presents an analysis of a singularly perturbed three-component FitzHugh-Nagumo model with a small jump-type heterogeneity. The authors consider pinned front solutions and pulse solutions for the model problem. Explicit conditions for the existence and stability of the pinned front solutions are demonstrated. For this, geometric singular perturbation techniques with an action functional approach are employed (the interested reader should also see [\textit{A. Doelman} et al., SIAM J. Appl. Dyn. Syst. 15, No. 2, 655--712 (2016; Zbl 1343.34041)]). One novelty in this article is the determination of particular parameter ranges where one can explicitly compute the pinning distance of a local defect solution. It should also be mentioned that local defect solutions were investigated numerically in [\textit{P. van Heijster} et al., Nonlinearity 24, No. 1, 127--157 (2011; Zbl 1208.35010)].