扩散的Beddington-DeAngelis捕食模型中空间异性的作用
The Effect of Spatial Heterogeneity on the Diffusion Beddington-DeAngelis Predator-Prey Model
摘要: 本文研究空间异性环境下具有Beddington-DeAngelis型功能反应函数的Leslie-Gower捕食模型。首先应用线性化方法分析半平凡解的稳定性，发现空间异性环境中半平凡解的稳定性会随扩散系数的变化而改变。其次应用局部分支定理讨论正平衡解的存在性，并对分支方向和分支解的稳定性进行刻画。
Abstract: In this paper, we study the Leslie-Gower predator-prey model with Beddington-DeAngelis type functional response in the spatially heterogeneous environment. First, the linearization method is used to analyze the stability of the semi-trivial solutions. It is found that the stability of the semi-trivial solution in the spatially heterogeneous environment will change with the diffusion coefficient varies. Secondly, the local bifurcation theory is used to discuss the existence of the positive steady state solution, and the bifurcation direction and the stability of bifurcation solution are investigated.
文章引用：郝雅婷, 张丽娜. 扩散的Beddington-DeAngelis捕食模型中空间异性的作用[J]. 应用数学进展, 2021, 10(12): 4469-4476. https://doi.org/10.12677/AAM.2021.1012475

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