具有MICHAELIS-MENTEN饱和函数的趋化模型斑图分析  

Pattern Analysis of Chemotaxis Model with MICHAELISMENTEN Saturation Function

作　　者：袁蕾 段震鸣 许震宇[1] 夏鹏 YUAN Lei;DUAN Zhenming;XU Zhenyu;XIA Peng(Wuxi Tourism and Trade Branch,Jiangsu Union Technical Institute,Wuxi 214045,Jiangsu)

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：《湖南工业职业技术学院学报》2023年第2期15-19,共5页Journal of Hunan Industry Polytechnic

基　　金：江苏省陶行知研究会一般课题(项目编号:JSTY14257);无锡旅游商贸高等职业技术学校校级专项课题(项目编号:WXLS/ZX/2022/03)。

摘　　要：针对一类具有MICHAELIS-MENTEN饱和函数的趋化模型斑图存在性,利用偏微分方程线性稳定性理论,通过对模型的常数定态解进行稳定性研究,得到了模型斑图存在的条件。利用数值研究证明了非常数解的存在性,分析了模态与斑图解之间的关系,并从数值上验证了该模型具有亚稳性结构。Aiming at the existence of patterns in a class of chemotactic models with the MICHAELIS-MENTEN saturation function,using the theory of linear stability of partial differential equations,the conditions for the existence of pattern patterns in the model have been obtained by studying the stability of the model's constant and stationary solutions.And,using numerical research to prove the existence of non-constant solutions,analyzing the relationship between mode and pattern,and numerically verifying that the model has a metastable structure.

关 键 词：斑图 常数定态解 稳定性 饱和函数 趋化模型 

分 类 号：O193[理学—数学]