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Autori principali: Pettersson, Irina, Rybalko, Antonina, Rybalko, Volodymyr
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2503.18477
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author Pettersson, Irina
Rybalko, Antonina
Rybalko, Volodymyr
author_facet Pettersson, Irina
Rybalko, Antonina
Rybalko, Volodymyr
contents We present a derivation of a multidomain model for the electric potential in bundles of randomly distributed axons with different radii. The FitzHugh-Nagumo dynamics is assumed on the axons' membrane, and the conductivity depends nonlinearly on the electric field. Under ergodicity conditions, we study the asymptotic behavior of the potential in the bundle when the number of the axons in the bundle is sufficiently large and derive a macroscopic multidomain model describing the electrical activity of the bundle. Due to the randomness of geometry, the effective intracellular potential is not deterministic but is shown to be a stationary function with realizations that are constant on axons' cross sections. The technique combines the stochastic two-scale convergence and the method of monotone operators.
format Preprint
id arxiv_https___arxiv_org_abs_2503_18477
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Nonlinear multidomain model for nerve bundles with random structure
Pettersson, Irina
Rybalko, Antonina
Rybalko, Volodymyr
Analysis of PDEs
We present a derivation of a multidomain model for the electric potential in bundles of randomly distributed axons with different radii. The FitzHugh-Nagumo dynamics is assumed on the axons' membrane, and the conductivity depends nonlinearly on the electric field. Under ergodicity conditions, we study the asymptotic behavior of the potential in the bundle when the number of the axons in the bundle is sufficiently large and derive a macroscopic multidomain model describing the electrical activity of the bundle. Due to the randomness of geometry, the effective intracellular potential is not deterministic but is shown to be a stationary function with realizations that are constant on axons' cross sections. The technique combines the stochastic two-scale convergence and the method of monotone operators.
title Nonlinear multidomain model for nerve bundles with random structure
topic Analysis of PDEs
url https://arxiv.org/abs/2503.18477