交错扩散对具有保护区域的Beddington-DeAngelis型捕食模型共存解的影响  

The Effect of Cross-Diff on Beddington-DeAngelis Type Predator-Prey Model with Protection Zone

作　　者：闫凯 张丽娜 蔺娜娜 

机构地区：[1]西北师范大学数学与统计学院, 甘肃 兰州

出　　处：《理论数学》2021年第5期841-850,共10页Pure Mathematics

摘　　要：本文研究齐次 Neumann边界条件下交错扩散对具有保护区域的 Beddington-DeAngelis 型捕食模型共存解的影响, 其中交错扩散表示食饵躲避猎物. 首先应用线性化方法分析非负常数平衡解的稳定性. 其次应用最大值原理给出正解的先验估计. 最后应用分歧理论讨论共存解的存在性. 结果表明, 交错扩散有助于物种的共存。The effect of cross-diffusion on Beddington-DeAngelis type predator-prey model with protection zone and the homogeneous Neumann boundary conditions is considered, where the cross-diffusion represents the tendency of prey to keep away from its predator. Firstly, the stability of the nonnegative constant steady state solutions is analyzed by the linearization method. Secondly, a priori estimates of positive steady state solutions is given by applying maximum principle. Finally, the existence of coexistence solutions is discussed by using bifurcation theory. As a result, it is shown that the cross-diffusion is beneficial for species coexistence.

关 键 词：捕食模型 Beddington-DeAngelis 型功能反应函数 保护区域 交错扩散 共存解 

分 类 号：O17[理学—数学]