Analysis and stability of the FitzHugh-Nagumo system with rapidly oscillating Neumann boundary condition
Year: 2026
Type: preprint
Abstract: In this paper we study the FitzHugh-Nagumo system posed on the half-line with a sinusoidal forcing term acting at the origin through the Neumann boun\-da\-ry condition. By applying an averaging method, we show that, if the frequency of the oscillating forcing is high enough, then the system can be approximated by a combination of a highly-oscillatory term and the solution of a simpler system. This approach allows us to establish stability results under persistent time-varying boundary conditions. Along with the averaging method, we use an adaptation of the contracting rectangles method, tailored to handle parabolic equations with spatially and temporally varying coefficients.
Source: arXiv (Cornell University)
Authors: Rodriguez, Alexander, Cerpa, Eduardo
Institution: Pontificia Universidad Católica de Chile
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212152839