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A Stage-Structure Predator-Prey Model with Ratio-Dependent Functional Response and Anti-Predator

机译：具有比率依赖功能响应和抗捕食者的舞台结构捕食者 - 猎物模型

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This article discusses a stage-structure predator-prey model with ratio-dependent functional response. The proposed mathematical model is a system of three nonlinear ordinary differential equations that describes the interactions between prey population, juvenile predator, and adult predator. It is assumed that only adult predators attack and consume the prey and have the ability to reproduce. Here, we also consider an anti-predator defense effects where prey can attack juvenile predator. However. it is also assumed that adult predators may help when juvenile predators are attacked by prey. The proposed model is analyzed dynamically, which includes the existence and local stability of equilibrium points. There are two equilibria, namely the predator extinction point and the co-existence point. The predator extinction point is always there but it is conditionally stable. If there exists a co-existence point, then this point is also conditionally stable. Numerical solutions are carried out to illustrate the theoretical results.
机译：本文讨论了具有比率相关功能响应的舞台结构捕食者 - 猎物模型。所提出的数学模型是三个非线性常微分方程的系统，其描述了猎物群，少年捕食者和成人捕食者之间的相互作用。假设只有成人捕食者攻击并消耗猎物并有能力重现。在这里，我们还考虑猎物可以攻击少年捕食者的反捕食者防御效果。然而。还假设成人捕食者可能有助于少年捕食者被猎物袭击。该提出的模型是动态分析的，这包括均衡点的存在和局部稳定性。有两个均衡，即捕食者灭绝点和共存点。捕食者灭绝点始终存在，但有条件稳定。如果存在共存点，则该点也有条件稳定。进行数值解决方案以说明理论结果。

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