REMARKS ON PATTERN FORMATION IN A MODEL FOR HAIR FOLLICLE SPACING

被引：1

作者：

Rashkov, Peter ^{[1
]}

机构：

[1] Univ Marburg, Dept Math & Informat, D-35032 Marburg, Germany

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2015年 / 20卷 / 05期

关键词：

Biological modelling; pattern formation; dynamical systems; Turing instability; far-from-equilibrium solutions; GLOBAL EXISTENCE; ACTIVATOR; EQUATIONS; SYSTEMS; GIERER;

D O I：

10.3934/dcdsb.2015.20.1555

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A modified version of the Gierer-Meinhardt reaction-diffusion system (without source terms) is used in a model for hair follicle spacing in mice, proposed by Sick, Reinker, Timmer and Schlake [22]. Global existence of solutions of this model system is shown by computing uniform bounds. Analysis of conditions for emergence of spatially heterogeneous solutions is performed using a limiting form of the original reaction-diffusion system. The conditions for pattern formation given in [22] are improved by including those subregions in the parameter space where far-from-equilibrium heterogeneous solutions occur.

引用

页码：1555 / 1572

页数：18

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