Global qualitative analysis of a discrete host‐parasitoid model with refuge and strong Allee effects
Global qualitative analysis of a discrete host‐parasitoid model with refuge and strong Allee effects
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DOI：
10.1002/mma.4731
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发表时间：
2018-03
影响因子：
2.9
通讯作者：
Daiyong Wu;Hongyong Zhao
中科院分区：
文献类型：
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作者：
Daiyong Wu;Hongyong Zhao
在本文中，我们讨论了一个离散寄主-拟寄主模型的定性行为，其中寄主受到避难和强Allee效应的影响。更准确地说，我们研究了宿主受避难或避难和强Allee效应影响的模型的局部和全局渐近稳定性、边界平衡点的稳定流形和不稳定流形、正平衡点的存在性和唯一性、正平衡点的局部和全局行为以及模型的一致持续性。并证明了该模型在边界平衡点的小邻域内发生跨临界分岔。一些数值模拟结果支持了我们的理论结果。结果表明，保护区的建立可能使拟寄生物灭绝，而寄生物存活，或使寄生物与拟寄生物的相互作用趋于稳定；避难区和强狭巷效应的增加对两种种群的共存有消极或积极的影响。
In this paper, we discuss the qualitative behavior of a discrete host‐parasitoid model with the host subject to refuge and strong Allee effects. More precisely, we study the local and global asymptotic stability, stable manifolds and unstable manifolds of boundary equilibrium points, existence and unique positive equilibrium point, local and global behavior of the positive equilibrium point, and the uniform persistence for the model with the host subject to the refuge or both refuge and strong Allee effects. It is also proved that the model undergoes a transcritical bifurcation in a small neighborhood of the boundary equilibrium point. Some numerical simulations are given to support our theoretical results. We can obtain that the addition of the refuge may make the parasitoids go extinct while the hosts survive or may stabilize the host‐parasitoid interaction; the addition of both refuge and strong Allee effects has either a negative or positive impact on the coexistence of both populations.