Degn-Harrison反应扩散系统的分支分析  

Bifurcation analysis of Degn-Harrison reaction-diffusion system

作　　者：刘晓慧 薛旭东 李兵方[2] LIU Xiaohui;XUE Xudong;LI Bingfang(Department of Basic Course,Shaanxi Railway Institute,Weinan 714000,China;School of Railway Equipment Manufacturing,Shaanxi Railway Institute,Weinan 714000,China)

机构地区：[1]陕西铁路工程职业技术学院基础课部,陕西渭南714000 [2]陕西铁路工程职业技术学院铁道装备制造学院,陕西渭南714000

出　　处：《陕西理工大学学报（自然科学版）》2024年第4期58-66,共9页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：陕西铁路工程职业技术学院科研项目(KY2022-48)。

摘　　要：在齐次Neumann边界条件下研究了一类Degn-Harrison反应扩散系统的分支问题。首先,利用中心流形定理和规范型理论确定了Hopf分支的稳定性和方向。其次,以扩散系数d 1为讨论参数,利用分支理论建立了扩散系统在单特征值处和双特征值处的分支结构。结果表明:扩散效应会影响反应系统的动力学行为,如果氧气扩散较快或者营养物扩散较慢,系统可能会出现周期振荡现象。The bifurcation problem of a Degn-Harrison reaction-diffusion system was studied under homogeneous Neumann boundary conditions.Firstly,the direction and stability of Hopf bifurcation of diffusion system were determined by the normal form theory and the central manifold theorem.Secondly,taking the diffusion coefficient d 1 as the discussion parameter,the existence of steady-state bifurcation at single and double eigenvalues of the diffusion system was given by applying bifurcation theory.The results indicate that diffusion effects can influence the dynamic behavior of the reaction system and that if oxygen diffuses rapidly or nutrients diffuse slowly,the system may exhibit periodic oscillations.

关 键 词：Degn-Harrison反应扩散系统 HOPF分支 稳态分支 

分 类 号：O175.26[理学—数学]