Existence and Stability of Standing Spot Solutions in a Three-Component FitzHugh--Nagumo System in R^2
Existence and Stability of Standing Spot Solutions in a Three-Component FitzHugh--Nagumo System in R^2
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R^2 中三分量 FitzHugh--Nagumo 系统中站立点解的存在性和稳定性
DOI：
10.1137/21m144027x
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Hideo Ikeda
中科院分区：
文献类型：
--
作者：
関根 順;Hideo Ikeda
本文用解析奇异摄动技术对三分量Fitzhugh-Nagumo系统中关于驻点解的线性化本征值问题的本征值的位置给出了严格的数学证明。这一结果已经由[P.van Heijster和B.Sandstede，Phys.D，275(2014)，pp.19-34]，在形式渐近分析中，他们结合解析和数值方法，表明稳定的旅行斑解通过漂移分叉从稳定的站立解分叉出来。此外，我们的结果同时提供了对应于本征值的本征函数的近似。
This manuscript presents a mathematically rigorous proof for the location of eigenvalues of a linearized eigenvalue problem regarding standing spot solutions in a three-component FitzHugh–Nagumo system inusing an analytical singular perturbation technique. This result was already provided by [P. van Heijster and B. Sandstede,Phys. D,275 (2014), pp. 19–34] by formal asymptotic analysis, in which they showed that stable traveling spot solutions bifurcate from stable standing ones via a drift bifurcation by combining analytical and numerical methods. Moreover, our result simultaneously provides approximations of eigenfunctions corresponding to the eigenvalues.