依赖捕食者的复制者动力学或具有两种猎物类型和频率依赖性的捕食-猎物模型
Predator-dependent replicator dynamics or a predator-prey model with two prey types and frequency dependence
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中文总结 AI 辅助
研究具有两种猎物和一种捕食者的种群模型，可视为依赖捕食者适应性的复制者动力学或特定Lotka-Volterra型模型。通过新观点获平衡条件，证明相关定理，揭示参数固定时丰富分岔及多样物种共存情况。
中文摘要 AI 辅助
Braga和Wardil [《物理学报：数学理论》55 (2022) 025601] 引入了一个关于两种猎物物种的种群模型，它们相互竞争并被单一捕食者物种捕食。他们展示了16种动态情景的存在，并阐述了三种物种稳定共存的充分条件。该模型基于两个收益矩阵，可视为猎物具有依赖捕食者适应性的复制者动力学。我们认为该模型也可看作是具有单一猎物物种、猎物逻辑斯谛限制以及频率依赖繁殖和捕获系数的Lotka-Volterra型捕食-猎物模型。利用此观点，我们得到了三种个体平衡存在的条件。还证明了关于仅两种物种平衡稳定性或不稳定性的定理，并将这些平衡的稳定性变化与三种物种平衡的出现或消失相关联。当除调节承载能力的参数外所有参数固定时，可能会出现丰富的分岔级联。解的范围从因猎物不足导致捕食者灭绝到捕食者与一种或两种猎物类型共存，有时还会出现涉及所有物种的稳定极限环。
英文摘要
Braga and Wardil [J. Phys. A: Math. Theor. 55 (2022) 025601] introduced a population model for two prey species that compete among themselves and are preyed upon by a single predator species. They showed the existence of 16 dynamic scenarios and stated sufficient conditions for the stable coexistence of the three species. The model, which can be seen as replicator dynamics with predator-dependent fitnesses for the prey, is based on two pay-off matrices: one for prey reproduction and one for interaction between prey and predators. We argue that the model can also be seen as a Lotka-Volterra-type predator-prey model with a single prey species, logistic limitation for prey, and frequency-dependent reproduction and capture coefficients. Using this alternative viewpoint, we obtain conditions for the existence of equilibria with the three types of individuals. We also prove theorems on the stability or instability of equilibria with only two species and relate the stability change of these equilibria to the appearance or disappearance of equilibria with the three species. When all parameters, except the one that regulates carrying capacities, are fixed, a rich cascade of bifurcations may appear. Solutions range from predator extinction due to insufficient prey to predators coexisting with one or two prey types. Sometimes stable limit cycles involving all species appear.
