The objective is the study of the dynamics of a prey–predator model where the prey species can migrate between two patches. The specialist predator is confined to the first patch, where it consumes the prey following the simple law of mass action. The prey is further “endangered” in that it suffers from the strong Allee effect, assumed to occur due to the lowering of successful matings. In the second patch the prey grows logistically. The model is formulated in a comprehensive way so as to include specialist as well as generalist predators, as a continuum of possible behaviors. This model described by a set of three ordinary differential equation is an extension of some previous models proposed and analysed in the literature on metapopulation models. The following analysis issues will be addressed: boundedness of the solution, equilibrium feasibility and stability, and dynamic behaviour dependency of the population and environmental parameters. Three types for both equilibria and limit cycles are possible: trivial, predator-free and coexistence. Classical analysis techniques are used and also theoretical and numerical bifurcation analysis. Besides the well-known local bifurcations, also a homoclinic connection as a global bifurcation is calculated. In view of the difficulty in the analysis, only the specialist case will be analysed. The obtained results indicate that the safe harbor can protect the endangered species under certain parametric restrictions.

目的是研究捕食者－捕食者模型的动力学，其中猎物种类可以在两个斑块之间迁移。专业的捕食者被限制在第一个斑块中，在那里，它遵循简单的大规模行动定律消耗猎物。由于受到成功交配降低的影响，猎物会遭受强烈的Allee效应，因此进一步受到“威胁”。在第二个补丁中，猎物在逻辑上成长。该模型以一种综合的方式制定，以包括专家和通缉者，作为可能行为的连续体。由一组三个常微分方程描述的模型是对一些先前模型的扩展，这些模型是在有关人口模型的文献中提出和分析的。将解决以下分析问题：解决方案的边界，平衡的可行性和稳定性，以及种群和环境参数的动态行为依赖性。平衡周期和极限周期的三种类型都是可能的：琐碎的，无掠食性的和共存的。使用经典分析技术以及理论和数值分叉分析。除了众所周知的局部分叉，还计算了作为整体分叉的同宿连接。鉴于分析的困难，仅对专家案例进行分析。获得的结果表明，安全港可以在某些参数限制下保护濒危物种。使用经典分析技术以及理论和数值分叉分析。除了众所周知的局部分叉，还计算了作为整体分叉的同宿连接。鉴于分析的困难，仅对专家案例进行分析。获得的结果表明，安全港可以在某些参数限制下保护濒危物种。使用经典分析技术以及理论和数值分叉分析。除了众所周知的局部分叉，还计算了作为整体分叉的同宿连接。鉴于分析的困难，仅对专家案例进行分析。获得的结果表明，安全港可以在某些参数限制下保护濒危物种。