Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion

被引：13

作者：

Zemskov, E. P. ^{[1
,2
]}

Epstein, I. R. ^{[1
,2
]}

Muntean, A. ^{[3
]}

机构：

[1] Brandeis Univ, Dept Chem, Waltham, MA 02454 USA

[2] Russian Acad Sci, Ctr Comp, Moscow 119333, Russia

[3] Tech Univ Eindhoven, Dept Math & Comp Sci, Inst Complex Mol Syst, NL-5600 MB Eindhoven, Netherlands

来源：

MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA | 2011年 / 28卷 / 02期

基金：

俄罗斯基础研究基金会; 美国国家科学基金会;

关键词：

cross-diffusion; reaction-diffusion systems; pulse solutions; pattern formation; TRAVELING-WAVE SOLUTIONS;

D O I：

10.1093/imammb/dqq012

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We study FitzHugh-Nagumo type reaction-diffusion systems with linear cross-diffusion terms. Based on an analytical description using piecewise linear approximations of the reaction functions, we completely describe the occurrence and properties of wavy pulses, patterns of relevance in several biological contexts, in two prototypical systems. The pulse wave profiles arising in this treatment contain oscillatory tails similar to those in travelling fronts. We find a fundamental, intrinsic feature of pulse dynamics in cross-diffusive systems-the appearance of pulses in the bistable regime when two fixed points exist.

引用

页码：217 / 226

页数：10

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