arXiv subjects

Afroditi Talidou

Publications and source records attributed to Afroditi Talidou.

2 recordsLinked to original sources

arXiv2025

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.

math.AP↗

arXiv2020

Near-Pulse Solutions of the FitzHugh-Nagumo Equations on Cylindrical Surfaces

We introduce a geometrical extension of the FitzHugh-Nagumo equations describing propagation of electrical impulses in nerve axons. In this extension, the axon is modeled as a warped cylinder, rather than a straight line, as is usually done, while pulses propagate on its surface, as is the case with real axons. We prove the stability of electrical impulses for a standard cylinder and existence and stability of pulse-like solutions for warped cylinders whose radii are small and vary slowly along their lengths.

math.AP↗