Pattern formation of a Schnakenberg-type plant root hair initiation model

被引：1
作者：
Li, Yanqiu [1 ]
Jiang, Juncheng [1 ]
机构：
[1] Nanjing Univ Technol, Puzhu S Rd, Nanjing 211816, Jiangsu, Peoples R China
来源：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2018年 / 88期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Schnakenberg-type model; pattern formation; global bifurcation; steady state solution; Hopf bifurcation; Turing bifurcation; STEADY-STATE SOLUTIONS; BIFURCATION-ANALYSIS; GLOBAL BIFURCATION; DIFFUSION; BRUSSELATOR; GLYCOLYSIS; EXISTENCE; DYNAMICS; SYSTEMS; BOUNDS;
D O I：
10.14232/ejqtde.2018.1.88
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper concentrates on the diversity of patterns in a quite general Schnakenberg-type model. We discuss existence and nonexistence of nonconstant positive steady state solutions as well as their bounds. By means of investigating Turing, steady state and Hopf bifurcations, pattern formation, including Turing patterns, nonconstant spatial patterns or time periodic orbits, is shown. Also, the global dynamics analysis is carried out.
引用
收藏
页码：1 / 19
页数：19
相关论文
共 39 条
  • [21] Some nonexistence results for nonconstant stationary solutions to the Gray-Scott model in a bounded domain
    Peng, R.
    Wang, M. X.
    [J]. APPLIED MATHEMATICS LETTERS, 2009, 22 (04) : 569 - 573
  • [22] On stationary patterns of a reaction-diffusion model with autocatalysis and saturation law
    Peng, Rui
    Shi, Junping
    Wang, Mingxin
    [J]. NONLINEARITY, 2008, 21 (07) : 1471 - 1488
  • [23] Qualitative analysis of steady states to the Sel'kov model
    Peng, Rui
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 241 (02) : 386 - 398
  • [24] Positive steady-state solutions of the Sel'kov model
    Peng, Rui
    Wang, Mingxin
    Yang, Ming
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2006, 44 (9-10) : 945 - 951
  • [25] SIMPLE CHEMICAL-REACTION SYSTEMS WITH LIMIT-CYCLE BEHAVIOR
    SCHNAKENBERG, J
    [J]. JOURNAL OF THEORETICAL BIOLOGY, 1979, 81 (03) : 389 - 400
  • [26] SELF-OSCILLATIONS IN GLYCOLYSIS .1. A SIMPLE KINETIC MODEL
    SELKOV, EE
    [J]. EUROPEAN JOURNAL OF BIOCHEMISTRY, 1968, 4 (01): : 79 - &
  • [27] On global bifurcation for quasilinear elliptic systems on bounded domains
    Shi, Junping
    Wang, Xuefeng
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (07) : 2788 - 2812
  • [28] Numerical Results for Snaking of Patterns over Patterns in Some 2D Selkov-Schnakenberg Reaction-Diffusion Systems
    Uecker, Hannes
    Wetzel, Daniel
    [J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2014, 13 (01): : 94 - 128
  • [29] Global bifurcation analysis and pattern formation in homogeneous diffusive predator-prey systems
    Wang, Jinfeng
    Wei, Junjie
    Shi, Junping
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (04) : 3495 - 3523
  • [30] Wang M.X., 2010, Nonlinear Elliptic Equations
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