FitzHugh-Nagumo系统行波解的存在性及渐近性

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-08 DOI:10.1002/mma.10849

Xiaojie Lin, Chen Li, Zengji Du, Ke Wang

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引用次数: 0

摘要

本文讨论了FitzHugh-Nagumo系统行波解的存在性，该系统是研究神经冲动传播的可激模型。通过行波变换和时间尺度变换，将FitzHugh-Nagumo系统转化为奇异摄动微分系统。利用几何奇异摄动理论和Fredholm正交性，构造了相关行波方程的局部不变流形，得到了相关行波解的存在性。此外，我们还利用渐近理论讨论了行波解的渐近性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Existence and Asymptotic Behaviors of Traveling Wave Solutions for the FitzHugh–Nagumo System

In this paper, we are concerned with the existence of traveling wave solution for FitzHugh–Nagumo system, which is an excitable model for studying nerve impulse propagation. By using traveling wave transformation and time scale transformation, the FitzHugh–Nagumo system is transformed into a singularly perturbed differential system. We construct a locally invariant manifold for the associated traveling wave equation and obtain the existence of traveling wave solution by employing geometric singular perturbation theory and Fredholm orthogonality. Furthermore, we also discuss the asymptotic behaviors of the traveling wave solution by applying the asymptotic theory.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.