Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system

Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system

We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh–Nagumo system describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like...

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Main Authors: Aleksandra Gawlik, Vsevolod Vladimirov, Sergii Skurativskyi
Format: Article
Language:English
Published: Vilnius University Press 2020-05-01
Series:Nonlinear Analysis
Subjects:
effects of relaxation
modified FitzHugh–Nagumo model
traveling waves
solitary wave solutions
Online Access:https://www.journals.vu.lt/nonlinear-analysis/article/view/16842
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spelling doaj-b434b5b3180c4078a769d90e3f8ac5132020-11-25T02:06:22ZengVilnius University PressNonlinear Analysis1392-51132335-89632020-05-0125310.15388/namc.2020.25.16842Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo systemAleksandra Gawlik0Vsevolod Vladimirov1Sergii Skurativskyi2AGH University of Science and TechnologyAGH University of Science and TechnologySubbotin Institute of Geophysics, NAS of Ukraine We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh–Nagumo system describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like solutions under certain restrictions on the parameters. The results of theoretical studies are backed by the direct numerical simulation. https://www.journals.vu.lt/nonlinear-analysis/article/view/16842effects of relaxationmodified FitzHugh–Nagumo modeltraveling wavessolitary wave solutions
collection DOAJ
language English
format Article
sources DOAJ
author Aleksandra Gawlik
Vsevolod Vladimirov
Sergii Skurativskyi
spellingShingle Aleksandra Gawlik
Vsevolod Vladimirov
Sergii Skurativskyi
Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system
Nonlinear Analysis
effects of relaxation
modified FitzHugh–Nagumo model
traveling waves
solitary wave solutions
author_facet Aleksandra Gawlik
Vsevolod Vladimirov
Sergii Skurativskyi
author_sort Aleksandra Gawlik
title Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system
title_short Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system
title_full Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system
title_fullStr Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system
title_full_unstemmed Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system
title_sort existence of the solitary wave solutions supported by the modified fitzhugh–nagumo system
publisher Vilnius University Press
series Nonlinear Analysis
issn 1392-5113
2335-8963
publishDate 2020-05-01
description We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh–Nagumo system describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like solutions under certain restrictions on the parameters. The results of theoretical studies are backed by the direct numerical simulation.
topic effects of relaxation
modified FitzHugh–Nagumo model
traveling waves
solitary wave solutions
url https://www.journals.vu.lt/nonlinear-analysis/article/view/16842
work_keys_str_mv AT aleksandragawlik existenceofthesolitarywavesolutionssupportedbythemodifiedfitzhughnagumosystem
AT vsevolodvladimirov existenceofthesolitarywavesolutionssupportedbythemodifiedfitzhughnagumosystem
AT sergiiskurativskyi existenceofthesolitarywavesolutionssupportedbythemodifiedfitzhughnagumosystem
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