Homogeneity-Breaking Instability of Periodic Solutions of Gierer-Meindardt Model

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摘要 The homogeneity-breaking instability of the periodic solutions triggered by Hopf bifurcations of a diffusive Gierer-Meinhart system is studied in this paper.Sufficient conditions on the diffusion coefficients and the cross diffusion coefficients were derived to guarantee the occurrence of the aforementioned homogeneity-breaking instability.

作者 Aying Wan Zhiqiang Song Hongyan Lin Nan Xiang

机构地区 Department of Science and Technology School of Engineering School of Mathematics and Physics

出处《Journal of Harbin Institute of Technology(New Series)》 CAS 2024年第2期62-67,共6页 哈尔滨工业大学学报（英文版）

基金 Sponsored by the National Natural Science Foundation of China(Grant Nos.12061033,2020GG0130,2020MS04007,2020BS11,and NJZZ22286).

关键词 Gierer-Meindardt model CROSS-DIFFUSION homogeneity-breaking instability Hopf bifurcations

分类号 O29 [理学—应用数学]

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1万阿英,衣凤岐,郑立飞.一类扩散的Gierer-Meindardt的模型的振动模式和Hopf分支分析[J].数学物理学报（A辑）,2015,35(2):381-394. 被引量：5

二级参考文献10

1Turing A. The chemical basis of morphogenesis. Philos Trans Roy Soc London B, 1952, 237:37 72.
2Gierer A, Meinhardt H. A theory of biological pattern formation. Kybernetik, 1972, 12:30-39.
3Liu J, Yi F Q, Wei J J. Multiple bifurcation analysis and spatiotemporal patterns in a 1-d Gierer-Meinhardt model of morphogenesis. International Journal of Bifurcation and Chaos, 2010, 20:1007-1025.
4Ward M J, Wei J J. Hopf bifurcation of spike solutions for the shadow Gierer-Meinhardt model. Europ J Appl Math, 2003, 14:677-711.
5Ward M J, Wei J J. Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Journal of Nonlinear Sciences, 2003, 13:209-264.
6Yi F Q, Wei J J, Shi J P. Bifurcation and spatiotemporal patterns in a homogenous diffusive predator-prey system. Jour Diff Equa, 2009, 246:1944 1977.
7Chen S S, Shi J P. Global attractivity of equilibrium in Gierer-Meinhardt system with activator production saturation and gene expression time delays. Nonlinear Anal Real World Appl, 2013, 14:1871-1886.
8Chen S S , Shi J P, Wei J J. Bifurcation analysis of the Gierer-Meinhardt system with a saturation in the activator production. Appl Anal, 2014, 93(6): 1115-1134.
9Xu C, Wei J J. Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model. Nonlinear Anal RWA, 2012, 13:1961-1977.
10Liu P, Shi J P, Wang Y W, et al. Bifurcation analysis of reaction-diffusion Schnakenberg model. Jour Math Chem, 2013, 51:2001-2019.

共引文献4

1杨文彬,吴建华.空间齐次和非齐次下活化-抑制模型动力学分析[J].数学物理学报（A辑）,2017,37(2):390-400. 被引量：4
2李兵方,郭改慧,李艳玲.Degn-Harrison反应扩散系统的Turing不稳定性与Hopf分支[J].数学的实践与认识,2021,51(7):219-225. 被引量：1
3郭改慧,郭飞燕,刘晓慧.一类二重饱和可逆生化反应扩散模型的Hopf分支和Turing不稳定性[J].工程数学学报,2022,39(2):277-291. 被引量：1
4马亚妮,袁海龙.一类具有时滞的Gierer-Meinhardt活化抑制模型的分支分析[J].数学物理学报（A辑）,2023,43(6):1774-1788.

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Journal of Harbin Institute of Technology(New Series)

2024年第2期

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Homogeneity-Breaking Instability of Periodic Solutions of Gierer-Meindardt Model

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