一类时滞自催化可逆生化反应模型的Hopf分支及其稳定性

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (3): 147-152.

一类时滞自催化可逆生化反应模型的Hopf分支及其稳定性

郭飞燕, 郭改慧^*

陕西科技大学数学与数据科学学院, 陕西西安 710021

收稿日期:2022-04-20 出版日期:2023-06-28 发布日期:2023-07-07
通讯作者: 郭改慧(1979-),女,河南郑州人,博士,教授,博导. Email:guogaihui@sust.edu.cn
基金资助:
国家自然科学基金(61872227)

Hopf bifurcation and stability for an autocatalytic reversible biochemical reaction model with time delay

GUO Fei-yan, GUO Gai-hui

School of Mathematics & Data Science, Shaanxi University of Science and Technology, Xi’an 710021, China

Received:2022-04-20 Online:2023-06-28 Published:2023-07-07

摘要/Abstract

摘要： 基于Hopf分支理论,研究一类具有时滞效应的自催化三分子可逆生化反应模型.以时滞τ为参数,建立正常数平衡点的稳定性和Hopf分支的存在性.利用中心流形定理和规范型理论,给出Hopf的分支方向和稳定性判定条件.借助数值模拟,验证理论分析结果.

关键词: 可逆生化反应, Hopf分支, 稳定性, 时滞

Abstract: Based on the Hopf bifurcation theory, an autocatalytic three-molecular reversible biochemical reaction model with time delay is considered. First, the stability of the equilibrium and the existence of Hopf bifurcation are obtained by choosing the delay τ as parameter. Secondly, the direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the theoretical results.

Key words: reversible biochemical reaction, Hopf bifurcation, stability, delay

中图分类号:

O175.13

郭飞燕, 郭改慧. 一类时滞自催化可逆生化反应模型的Hopf分支及其稳定性[J]. 兰州理工大学学报, 2023, 49(3): 147-152.

GUO Fei-yan, GUO Gai-hui. Hopf bifurcation and stability for an autocatalytic reversible biochemical reaction model with time delay[J]. Journal of Lanzhou University of Technology, 2023, 49(3): 147-152.

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