一类自催化可逆生化反应模型的Hopf分支及其稳定性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 166-177.

一类自催化可逆生化反应模型的Hopf分支及其稳定性

郭改慧*(),刘晓慧

陕西科技大学文理学院西安 710021

收稿日期:2020-01-09 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 郭改慧 E-mail:guogaihui@sust.edu.cn
基金资助:
国家自然科学基金(61872227);国家自然科学基金(61672021);国家自然科学基金(11671243);国家自然科学基金(11901370);大学生创新创业训练计划(201910708010)

Hopf Bifurcation and Stability for an Autocatalytic Reversible Biochemical Reaction Model

Gaihui Guo*(),Xiaohui Liu

School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021

Received:2020-01-09 Online:2021-02-26 Published:2021-01-29
Contact: Gaihui Guo E-mail:guogaihui@sust.edu.cn
Supported by:
the NSFC(61872227);the NSFC(61672021);the NSFC(11671243);the NSFC(11901370);the National Undergraduate Innovation and Entrepreneurship Training Program(201910708010)

摘要/Abstract

摘要：

在齐次Neumann边界条件下，研究一类自催化可逆三分子生化反应模型.首先对常微分系统，给出Hopf分支的存在性及稳定性.其次对偏微分系统，建立由扩散系数引起的Turing不稳定性，同时给出Hopf分支的存在性，并利用规范型理论和中心流形定理建立Hopf分支的方向和稳定性.最后，借助Matlab软件进行数值模拟，验证补充理论分析结果.

关键词: 可逆生化反应, Turing不稳定性, Hopf分支, 稳定性

Abstract:

An autocatalytic reversible three-molecular biochemical reaction model subject to Neumann boundary conditions is considered. Firstly, the existence and stability of the Hopf bifurcation for the ordinary differential system are given. Secondly, the effect of diffusion coefficients on Turing instability is established and the existence of Hopf bifurcation is obtained for the partial differential system with diffusion. Then applying the normal form theory and center manifold theorem, the direction and stability of Hopf bifurcation are also given. Finally, some numerical simulations are carried out with the help of Matlab software to verify and supplement the theoretical results.

Key words: Reversible biochemical reaction, Turing instability, Hopf bifurcation, Stability

中图分类号:

O175.26

郭改慧,刘晓慧. 一类自催化可逆生化反应模型的Hopf分支及其稳定性[J]. 数学物理学报, 2021, 41(1): 166-177.

Gaihui Guo,Xiaohui Liu. Hopf Bifurcation and Stability for an Autocatalytic Reversible Biochemical Reaction Model[J]. Acta mathematica scientia,Series A, 2021, 41(1): 166-177.

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参考文献 13

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