Bogdanov-Takens Bifurcation of Codimension 3 in the Gierer-Meinhardt Model

被引：0
|
作者：
Wu, Ranchao [1 ]
Yang, Lingling [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2023年 / 33卷 / 14期
基金：
中国国家自然科学基金;
关键词：
Gierer-Meinhardt model; saddle-node; Hopf; Bogdanov-Takens bifurcation; PREDATOR-PREY SYSTEM;
D O I：
10.1142/S0218127423501638
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Bifurcation of the local Gierer-Meinhardt model is analyzed in this paper. It is found that the degenerate Bogdanov-Takens bifurcation of codimension 3 exists in the model, except for the saddle-node bifurcation and the Hopf bifurcation. That was not reported in the literature about this model. The existence of equilibria, their stability, the bifurcation and the induced complicated and interesting dynamics are explored in detail, by using stability analysis, normal form method and bifurcation theory. Numerical results are also presented to validate the theoretical results.
引用
收藏
页数：10
相关论文
共 50 条
  • [1] Bogdanov-Takens Bifurcation
    Liebscher, Stefan
    [J]. BIFURCATION WITHOUT PARAMETERS, 2015, 2117 : 81 - 102
  • [2] Codimension-Two Bifurcation Analysis on a Discrete Gierer-Meinhardt System
    Liu, Xijuan
    Liu, Yun
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (16):
  • [3] Degenerate Bogdanov-Takens bifurcation of codimension 4 in Holling-Tanner model with harvesting
    Xiang, Chuang
    Lu, Min
    Huang, Jicai
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 314 : 370 - 417
  • [4] ANALYSIS OF THE HOPF BIFURCATION IN A DIFFUSIVE GIERER-MEINHARDT MODEL
    Asheghi, Rasoul
    [J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2023, 62 (01) : 83 - 104
  • [5] Bogdanov-Takens bifurcation in a predator-prey model
    Liu, Zhihua
    Magal, Pierre
    Xiao, Dongmei
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2016, 67 (06):
  • [6] Stability and Hopf Bifurcation Analysis of a Reduced Gierer-Meinhardt Model
    Asheghi, Rasoul
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (10):
  • [7] BOGDANOV-TAKENS BIFURCATION OF CODIMENSION 3 IN A PREDATOR-PREY MODEL WITH CONSTANT-YIELD PREDATOR HARVESTING
    Huang, Jicai
    Liu, Sanhong
    Ruan, Shigui
    Zhang, Xinan
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (03) : 1041 - 1055
  • [8] Hopf bifurcation of spike solutions for the shadow Gierer-Meinhardt model
    Ward, MJ
    Wei, J
    [J]. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2003, 14 : 677 - 711
  • [9] Turing-Hopf Bifurcation in Diffusive Gierer-Meinhardt Model
    Yang, Rui
    Yu, Xiao-Qing
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2022, 32 (04):
  • [10] Improved Homoclinic Predictor for Bogdanov-Takens Bifurcation
    Kuznetsov, Yu. A.
    Meijer, H. G. E.
    Al Hdaibat, B.
    Govaerts, W.
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (04):
12345