具有饱和效应的自催化反应扩散模型的分支分析  

Bifurcation Analysis for an Autocatalysis Reaction-diffusion Model with Saturation Effect

作　　者：郭飞燕 郭改慧[1] GUO Feiyan;GUO Gaihui(School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi'an 710021,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《应用数学》2023年第3期578-588,共11页Mathematica Applicata

基　　金：国家自然科学基金(61872227)。

摘　　要：在齐次Neumann边界条件下研究一类带有饱和效应的任意阶自催化反应扩散模型.首先对常微分系统,给出正平衡点的稳定性,且以k为分支参数得到Hopf分支的存在性及稳定性.其次对扩散系统,建立由扩散引起的Turing不稳定性,同时当扩散系数满足一定条件时给出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,借助一些数值模拟实例,验证理论分析结果.An arbitrary order autocatalysis reaction-diffusion model with saturation effect subject to Neumann boundary conditions is considered.Firstly,the stability of the equilibrium for the ordinary differential system is given.Taking k as the bifurcation parameter,the existence and stability of Hopf bifurcation are obtained.Secondly,the effect of diffusion coefficients on Turing instability is given and the existence of Hopf bifurcation is obtained for the partial differential system.Then applying the normal form theory and center manifold theorem,the direction and stability of Hopf bifurcation are also given.Finally,some numerical simulation examples are used to verify the theoretical results.

关 键 词：饱和效应 自催化 Turing不稳定性 HOPF分支 

分 类 号：O175.26[理学—数学]