一类生化反应模型的Hopf分支及其稳定性  

Hopf Bifurcation and Stability for a Biochemical Reaction Model

作　　者：郭改慧[1] 王晓妮[1] 岳宗敏[1] 

机构地区：[1]陕西科技大学理学院,陕西西安710021

出　　处：《武汉大学学报（理学版）》2015年第6期568-572,共5页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金项目(11401356;11301314;11271236);陕西省自然科学基础研究计划资助项目(2015JM1008);陕西省教育厅自然科学专项科研计划资助项目(14JK1081)

摘　　要：研究一类多分子生化反应模型.针对常微分系统,给出了Hopf分支的存在性及稳定性.讨论了带扩散项的偏微分系统,在扩散系数满足一定条件时,得到Hopf分支的存在性,利用规范型理论和中心流形定理给出Hopf分支的方向及稳定性.借助Matlab软件进行数值模拟,验证了理论结果.A multi-molecule model in biochemistry reaction is investigated in this paper.Firstly,the existence and stability of Hopf bifurcation for the ordinary differential system are obtained.Secondly,the partial differential system with diffusion is discussed and the diffusion-driven Hopf bifurcation is derived.Applying the normal form theory and the center manifold theorem,the direction and stability of this Hopf bifurcation are also given.Finally,some numerical simulations resorting to Matlab software are presented to verify and supplement theoretical results.

关 键 词：生化模型 HOPF分支 稳定性 

分 类 号：O175.26[理学—数学]