In this article, we study the behavior of a nonlinear age-structured predator-prey model that is a generalization of Lotka-Volterra equations. We prove global existence, uniqueness and positivity of the solution using a semigroup approach. We make some analytically explicit thresholds that ensure, or not depending of their values, the boundedness of the solution and time asymptotic stability of equilibria. The latter theoretical results and their limits are enlightened by simulations.

中文翻译：

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年龄结构对Lotka Volterra方程动力学的影响

在本文中，我们研究了具有年龄结构的非线性捕食者－被捕食者模型的行为，该模型是Lotka-Volterra方程的推广。我们使用半群方法证明了该解的全局存在性，唯一性和正性。我们做出一些分析上明确的阈值，这些阈值可确保（或不取决于）它们的值，解的有界性和平衡的时间渐近稳定性。后面的理论结果及其局限性通过仿真得到了启发。