Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system
Articles
Aleksandra Gawlik
AGH University of Science and Technology
https://orcid.org/0000-0001-6899-7917
Vsevolod Vladimirov
AGH University of Science and Technology
Sergii Skurativskyi
Subbotin Institute of Geophysics, NAS of Ukraine
https://orcid.org/0000-0003-4944-2646
Published 2020-05-01
https://doi.org/10.15388/namc.2020.25.16842
PDF

Keywords

effects of relaxation
modified FitzHugh–Nagumo model
traveling waves
solitary wave solutions

How to Cite

GawlikA., VladimirovV. and SkurativskyiS. (2020) “Existence of the solitary wave solutions supported by the modified FitzHugh–Nagumo system”, Nonlinear Analysis: Modelling and Control, 25(3), pp. 482–501. doi: 10.15388/namc.2020.25.16842.

Abstract

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.

PDF
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Please read the Copyright Notice in Journal Policy