Approximation and stability results for the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources

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dc.catalogadorgrr
dc.contributor.authorCerpa Jeria, Eduardo Esteban
dc.contributor.authorCourdurier, Matías
dc.contributor.authorHernandez, Esteban
dc.contributor.authorMedina, Leonel E.
dc.contributor.authorPaduro Williamson, Esteban Andres
dc.date.accessioned2025-11-24T20:02:05Z
dc.date.available2025-11-24T20:02:05Z
dc.date.issued2025
dc.description.abstractThe use of high-frequency currents in neurostimulation has received increased attention in recent years due to its varied effects on tissues and cells. Neurons are commonly modeled as nonlinear systems, and questions such as stability can thus be addressed with well-known averaging methods. A recent strategy called interferential currents uses electrodes delivering sinusoidal signals of slightly different frequencies, and thus classical averaging (well-adapted to deal with a single frequency) cannot be directly applied. In this paper, we consider the one-dimensional FitzHugh-Nagumo system under the effects of a source composed of two terms that are sinusoidal in time and quadratically decaying in space. To study this setting we develop a new averaging strategy to prove that, when the frequencies involved are sufficiently high, the full system can be approximated by an explicit highly-oscillatory term plus the solution of a simpler -- albeit non-autonomous -- system. This decomposition can be seen as a stability result around a varying trajectory. One of the main novelties of the proofs presented here is an extension of the contracting rectangles method to the case of parabolic equations with space and time-depending coefficients.
dc.fechaingreso.objetodigital2025-11-24
dc.format.extent28 páginas
dc.fuente.origenWOS
dc.identifier.doi10.48550/arXiv.2305.00123
dc.identifier.urihttps://doi.org/10.48550/arXiv.2305.00123
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/107099
dc.information.autorucFacultad de Matemáticas; Paduro Williamson, Esteban Andres; 0000-0003-1769-0055; 1207276
dc.information.autorucFacultad de Matemáticas; Cerpa Jeria, Eduardo Esteban; 0000-0001-9974-324X; 1125488
dc.information.autorucFacultad de Matemáticas; Courdurier, Matías; 0000-0002-2161-0356; 1007892
dc.language.isoen
dc.nota.accesocontenido completo
dc.rightsacceso abierto
dc.subjectParabolic equations
dc.subjectNonlinear system
dc.subjectAveraging
dc.subjectContracting rectangles
dc.subjectInterferential currents
dc.subject.ddc600
dc.titleApproximation and stability results for the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources
dc.typepreprint
sipa.codpersvinculados1207276
sipa.codpersvinculados1125488
sipa.codpersvinculados1007892
sipa.trazabilidadWOS;2023-07-06
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