Stability of Traveling Fronts of the FitzHugh-Nagumo Equations on Cylindrical Surfaces

The FitzHugh-Nagumo equations are known to admit traveling front solutions in one spatial dimension that are nonlinearly stable. This paper concerns the stability of traveling front solutions propagating on cylindrical surfaces. It is shown that such traveling fronts are nonlinearly stable on the surface of standard cylinders of constant radius. The analysis is extended to warped cylinders with slowly varying radius, where persistence of front-like solutions is established. Numerical simulations support the theoretical findings.