具交叉扩散和弱Allee效应的反应扩散方程图灵斑图研究

Turing Pattern Study of Reaction Diffusion Equations with Cross Diffusion and Weak Allee Effect

本文提出了一类具有交叉扩散的反应扩散方程,用于研究一类具有弱Allee效应的捕食食饵反应扩散模型在交叉扩散驱动下的图灵斑图动力学现象。研究发现,交叉扩散是该模型产生图灵斑图必不可少的条件,如果没有交叉扩散,则模型不会发生图灵失稳。同时,通过选择不同参数,我们发现模型的斑图现象十分丰富,可以出现点斑图、点–线混合斑图、线斑图三种类型。

This article proposes a class of reaction diffusion equations with cross diffusion to study the Turing pattern dynamics of a predator-prey reaction diffusion model with weak Allee effect driven by cross diffusion. Research has found that cross diffusion is an essential condition for the model to generate Turing patterns. Without cross diffusion, the model will not experience Turing instability. At the same time, by selecting different parameters, we found that the pattern phenomenon of the model is very rich, which can appear in three types: spots pattern, spots-stripes mixed pattern and stripes pattern.