STEADY STATES OF FITZHUGH-NAGUMO SYSTEM WITH NON-DIFFUSIVE ACTIVATOR AND DIFFUSIVE INHIBITOR

被引：5

作者：

Li, Ying ^{[1
]}

Marciniak-Czochra, Anna ^{[2
,3
]}

Takagi, Izumi ^{[4
,5
]}

Wu, Boying ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 151000, Heilongjiang, Peoples R China

[2] Heidelberg Univ, Inst Appl Math, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

[3] Heidelberg Univ, Interdisciplinary Ctr Sci Comp IWR, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

[4] Renmin Univ China, Inst Math Sci, Beijing 100872, Peoples R China

[5] Tohoku Univ, Math Inst, Sendai, Miyagi 980857, Japan

来源：

TOHOKU MATHEMATICAL JOURNAL | 2019年 / 71卷 / 02期

关键词：

FitzHugh-Nagumo model; reaction-diffusion-ODE system; pattern formation; bifurcation analysis; steady states; global behaviour of solution branches; instability; ODE MODEL; STATIONARY SOLUTIONS; TURING INSTABILITY; PATTERNS;

D O I：

10.2748/tmj/1561082598

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a diffusion equation coupled to an ordinary differential equation with FitzHugh-Nagumo type nonlinearity. We construct continuous spatially heterogeneous steady states near, as well as far from, constant steady states and show that they are all unstable. In addition, we construct various types of steady states with jump discontinuities and prove that they are stable in a weak sense defined by Weinberger. The results are quite different from those for classical reaction-diffusion systems where all species diffuse.

引用

页码：243 / 279

页数：37

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