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

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.