一类密度抑制菌群效应模型局部分支研究  

A Study on Local Branching of a Model with Density Inhibiting Microbial Effect

作　　者：夏鹏 许震宇[1] XIA Peng;XU Zhenyu(Wuxi Tourism and Trade Branch,Jiangsu Union Technical Institute,Wuxi 214045,Jiangsu,China)

机构地区：[1]江苏联合职业技术学院无锡旅游商贸分院,江苏无锡214045

出　　处：《昆明冶金高等专科学校学报》2024年第2期78-85,共8页Journal of Kunming Metallurgy College

基　　金：江苏省陶行知研究会一般课题“基于多元表征的中职数学变式教学实践研究”(JSTY14257);无锡旅游商贸高等职业技术学校专项课题“课程思政视域下中职数学教学实践研究”(WXLS/ZX/2022/03)。

摘　　要：针对一类反应扩散模型,将物质分解速度β视为分支参数,通过微分方程线性理论找到空间均匀解不稳定的条件,即不稳定模态存在的条件;然后利用局部分支理论证明了系统局部分支的存在性;再利用渐近分析法和Fredholm原理,在常数解附近展开,得到模型在某一时刻非常数近似解;最后利用仿真分析,将得到的近似解与模型的真实解进行比较,验证理论的正确性。For a type of reaction diffusion model,the rate of material decomposition is considered as a branching parameter,and the conditions for the instability of spatially uniform solutions are found through linear theory of differential equations,that is,the conditions for the existence of unstable modes.Then,the local branch theory was used to prove the existence of local branches in the model.Secondly,by using the asymptotic analysis method,the model is expanded near the constant solution and studied using the Fredholm principle to obtain a non-constant approximate solution at a certain moment.Finally,using simulation analysis,the approximate solution obtained is compared with the actual solution of the model to verify the correctness of the theory.

关 键 词：局部分支 渐近分析 非常数解 近似解 

分 类 号：O193[理学—数学]