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Analysis and stability of the FitzHugh-Nagumo system with rapidly oscillating Neumann boundary condition

  • Alexander Rodriguez
  • Eduardo Cerpa
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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.

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Cite

BibTeXRIS
BibTeX
@misc{rodriguez2026analysis,
  title = {{Analysis and stability of the FitzHugh-Nagumo system with rapidly oscillating Neumann boundary condition}},
  author = {Alexander Rodriguez and Eduardo Cerpa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09636},
  eprint = {2609.09636},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09636},
}
RIS
TY  - UNPB
TI  - Analysis and stability of the FitzHugh-Nagumo system with rapidly oscillating Neumann boundary condition
AU  - Alexander Rodriguez
AU  - Eduardo Cerpa
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09636
UR  - https://arxiv.org/abs/2609.09636
AB  - 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.
ER  -