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

共 50 条

[21] Phase-field theory for Fitzhugh-Nagumo-type systems [J].

Soravia, P ;

Souganidis, PE .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (05) :1341-1359

[22] Global solvability of a class of reaction-diffusion systems with cross-diffusion [J].

Wang, Zhi-An ;

Wu, Leyun .

APPLIED MATHEMATICS LETTERS, 2022, 124

[23] Understanding the dual effects of linear cross-diffusion and geometry on reaction-diffusion systems for pattern formation [J].

Sarfaraz, Wakil ;

Yigit, Gulsemay ;

Barreira, Raquel ;

Remaki, Lakhdar ;

Alhazmi, Muflih ;

Madzvamuse, Anotida .

CHAOS SOLITONS & FRACTALS, 2024, 186

[24] On a class of Keller-Segel chemotaxis systems with cross-diffusion [J].

Xiang, Tian .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (08) :4273-4326

[25] Envelope Quasisolitons in Dissipative Systems with Cross-Diffusion [J].

Biktashev, V. N. ;

Tsyganov, M. A. .

PHYSICAL REVIEW LETTERS, 2011, 107 (13)

[26] Negative refractoriness in excitable systems with cross-diffusion [J].

Tsyganov M.A. ;

Biktashev V.N. ;

Ivanitsky G.R. .

Biophysics, 2009, 54 (4) :513-518

[27] STABILITY ESTIMATES FOR SYSTEMS WITH SMALL CROSS-DIFFUSION [J].

Alasio, Luca ;

Bruna, Maria ;

Capdeboscq, Yves .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2018, 52 (03) :1109-1135

[28] Stochastic Models for Nonlinear Cross-Diffusion Systems [J].

Belopolskaya, Yana .

STATISTICS AND SIMULATION, IWS 8 2015, 2018, 231 :145-159

[29] Heterogeneity-induced effects for pulse dynamics in FitzHugh-Nagumo-type systems [J].

Chen, Chao-Nien ;

Ei, Shin-Ichiro ;

Tzeng, Shyuh-Yaur .

PHYSICA D-NONLINEAR PHENOMENA, 2018, 382 :22-32

[30] Reduced order modelling of nonlinear cross-diffusion systems [J].

Karasozen, Bulent ;

Mulayim, Gulden ;

Uzunca, Murat ;

Yildiz, Suleyman .

APPLIED MATHEMATICS AND COMPUTATION, 2021, 401

← 1 2 3 4 5 →