SIAM Journal on Applied Mathematics, Volume 80, Issue 6, Page 2631-2656, January 2020.
We present, analyze, and simulate a model for predator-prey interaction structured by hunger. The model consists of a nonlocal transport equation for the predator, coupled to an ordinary differential equation for the prey. We deduce a system of 3 ODEs for some integral quantities of the transport equation, which generalizes some classical Lotka--Volterra systems. By taking an asymptotic regime of fast hunger variation, we find that this system provides new interpretations of classical Holling-type functional responses. We also show that, with a small extension, the system can reproduce predator-prey role reversal bistability results observed in the literature. We next establish a well-posedness result for the nonlocal transport equation. Finally, we show that in the basin of attraction of the nontrivial equilibrium, the asymptotic behavior of the original coupled PDE-ODE system is completely described by solutions of the ODE system.

中文翻译：

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具有饥饿结构的食肉动物与猎物的相互作用

SIAM应用数学杂志，第80卷，第6期，第2631-2656页，2020年1月。
我们提出，分析和模拟一个由饥饿构成的捕食者与猎物相互作用的模型。该模型包括捕食者的非局部运输方程，以及捕食者的常微分方程。我们为运输方程的某些整数推导了一个由3个ODE组成的系统，该系统推广了一些经典的Lotka-Volterra系统。通过采用快速饥饿变化的渐近机制，我们发现该系统为经典Holling型功能响应提供了新的解释。我们还表明，通过少量扩展，该系统可以重现文献中观察到的捕食者－被捕者角色逆转双稳态结果。接下来，我们为非局部输运方程建立一个适定性结果。最后，我们表明，在非平凡平衡吸引域中，