NONLINEAR STABILITY OF PULSE SOLUTIONS FOR THE DISCRETE FITZHUGH-NAGUMO EQUATION WITH INFINITE-RANGE INTERACTIONS

被引：17

作者：

Schouten-straatman, Willem M. ^{[1
]}

Hupkes, Hermen Jan ^{[1
]}

机构：

[1] Leiden Univ, Math Inst, POB 9512, Leiden, Netherlands

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 09期

关键词：

Lattice differential equations; FitzHugh-Nagumo system; infinite-range interactions; nonlinear stability; non-standard implicit function theorem; REACTION-DIFFUSION SYSTEMS; TRAVELING-WAVES; OSCILLATORY TAILS; BIFURCATIONS; EXISTENCE; OPERATORS; MOTION;

D O I：

10.3934/dcds.2019205

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we need to study a functional differential equation of mixed type (MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and phase spaces, by building on a technique developed by Bates, Chen and Chmaj for the discrete Nagumo equation. This allows us to transfer several crucial Fredholm properties from the PDE setting to our discrete setting.

引用

页码：5017 / 5083

页数：67

共 15 条

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[15] A remark on the existence of breather solutions for the discrete nonlinear Schrodinger equation in infinite lattices: The case of site-dependent anharmonic parameters
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