The effects of simple density-dependent prey diffusion and refuge in a predator-prey system
The effects of simple density-dependent prey diffusion and refuge in a predator-prey system
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DOI：
10.1016/j.jmaa.2021.124983
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发表时间：
2019-12
影响因子：
1.3
通讯作者：
Leoncio Rodriguez Q.;Jia Zhao;Luis F. Gordillo
中科院分区：
文献类型：
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作者：
Leoncio Rodriguez Q.;Jia Zhao;Luis F. Gordillo
本文研究了一个空间（二维）Rosenzweig-MacArthur模型，假设：（1）食饵扩散遵循非线性扩散规律，（2）食饵有一个捕食者不能进入的避难区（有时称为“保护区”），（3）捕食者遵循线性扩散规律。我们提出了一个分支分析系统，显示在稳定状态下的正解的存在性。我们补充的理论结果与数值计算和比较我们的结果与线性扩散的情况下获得的猎物运动。我们的结果表明，这两个模型，与线性和非线性扩散的猎物，有相同的分歧点和正解曲线几乎是相同的，在这个点的邻域，但他们得到显着不同的分歧参数接近零。
We study a spatial (two-dimensional) Rosenzweig-MacArthur model under the following assumptions: (1) prey spread follows a nonlinear diffusion rule, (2) preys have a refuge zone (sometimes called “protection zone”) where predators cannot enter, (3) predators move following linear diffusion. We present a bifurcation analysis for the system that shows the existence of positive solutions at the steady state. We complement the theoretical results with numerical computations and compare our results with those obtained in the case of having linear diffusion for the prey movement. Our results show that both models, with linear and nonlinear diffusion for the prey, have the same bifurcation point and the positive solution curves are virtually the same in a neighborhood of this point, but they get drastically different as the bifurcation parameter approaches zero.