MULTIPLE BIFURCATION ANALYSIS AND SPATIOTEMPORAL PATTERNS IN A 1-D GIERER-MEINHARDT MODEL OF MORPHOGENESIS

被引：34
作者：
Liu, Jianxin [1 ]
Yi, Fengqi [2 ]
Wei, Junjie [1 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China
[2] Harbin Engn Univ, Dept Appl Math, Harbin 150001, Heilongjiang, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Morphogenesis; pattern formation; diffusive Gierer-Meinhardt model; Hopf bifurcation; steady state bifurcation; POSITIVE STEADY-STATES; PREDATOR-PREY SYSTEM; SPIKE SOLUTIONS; EXISTENCE; GENERATION; STABILITY;
D O I：
10.1142/S0218127410026289
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A reaction-diffusion Gierer-Meinhardt model of morphogenesis subject to Dirichlet fixed boundary condition in the one-dimensional spatial domain is considered. We perform a detailed Hopf bifurcation analysis and steady state bifurcation analysis to the system. Our results suggest the existence of spatially nonhomogenous periodic orbits and nonconstant positive steady state solutions, which imply the possibility of complex spatiotemporal patterns of the system. Numerical simulations are carried out to support our theoretical analysis.
引用
收藏
页码：1007 / 1025
页数：19
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