AI 中文总结
研究具有年龄结构资源的模型中竞争种群的动态，通过积分半群理论等建立模型性质，借助李雅普诺夫泛函等刻画渐近动力学。结果表明除竞争排斥外，系统能呈现全局渐近稳定共存，由年龄介导的生态位划分机制导致。
AI 中文摘要
本文引入并分析了一个模型，其中一种共享的、具有年龄结构的资源被两个竞争种群通过依赖年龄的相互作用核进行开发利用。它为研究流行病学、免疫学和生态学中资源介导的竞争提供了一个通用框架。我们用积分半群理论建立了模型的适定性及其基本性质，包括正性和全局吸引子的存在性。然后，通过李雅普诺夫泛函、持久性结果和广义拉萨尔原理，我们根据竞争者的基本再生数和入侵适合度全面刻画了渐近动力学。我们的结果表明，除了经典的竞争排斥外，该系统还能表现出全局渐近稳定的共存，这一结果由年龄介导的生态位划分机制所允许。
英文摘要
In this paper, we introduce and analyse a model in which a shared, age-structured resource is exploited by two competing populations through age-dependent interaction kernels. It provides a general framework for studying resource-mediated competition in epidemiology, immunology and ecology. We use integrated semigroups theory to establish the well-posedness of the model and its fundamental properties, including positivity and the existence of a global attractor. Then, by means of Lyapunov functionals, persistence results and generalised LaSalle principle, we fully characterize the asymptotic dynamics in terms of the competitors's basic reproduction numbers and invasive fitnesses. Our results demonstrate that in addition to the classical competitive exclusion, the system can exhibit globally asymptotically stable coexistence, an outcome allowed by a mechanism of age-mediated niche partitioning.
