ABSTRACT

This paper is concerned about a diffusive degenerate predator–prey model with Beddington–DeAngelis functional response subject to homogeneous Neumann boundary condition. First, the global bifurcation branches of positive stationary solutions are studied, which are quite different from those with different degeneracy or functional response. Second, the multiplicity and stability of positive stationary solutions are obtained as the parameter k or m in the Beddington–DeAngelis functional response is large enough, from which the effects of the functional response on the coexistence region are revealed. In particular, the global stability of the positive stationary solution is derived as it exists uniquely.

摘要

本文关注的是受齐次 Neumann 边界条件约束的具有 Beddington-DeAngelis 函数响应的扩散退化捕食者 - 猎物模型。首先，研究了正平稳解的全局分岔分支，这些分支与具有不同简并或功能响应的分支有很大不同。其次，当 Beddington-DeAngelis 函数响应中的参数k或m足够大时，获得了正平稳解的多重性和稳定性，由此揭示了函数响应对共存区域的影响。特别是，正稳态解的全局稳定性是由于它唯一存在而导出的。