Title: Stabilization by Harvesting in Age-Structured Trophic Networks Show Chinese title

Title: 按年龄结构的营养级网络中的捕获稳定化

Abstract: We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, and others). The formulation incorporates nonlocal intra- and interspecific interactions modulated by environmental covariates. Under general assumptions on mortality, reproduction rates, and interaction kernels, we establish existence, uniqueness, and positivity of solutions. We illustrate the model's practical relevance along two lines. First, multi-species examples, notably a non-transitive (cyclic) competition model, for which we show that, under the model assumptions, a control applied to a single species can achieve global stabilization of the system. Second, the population dynamics of malaria-vector mosquitoes, for which we develop two control strategies (biological and genetic). In the biological-control scenario, we prove global asymptotic stability of the aquatic compartment by constructing an explicit Lyapunov function. Numerical simulations validate the theoretical results and compare the effectiveness of the proposed strategies in reducing vector density and malaria transmission. Show Chinese abstract

Abstract: 我们提出并分析了一个非线性年龄结构的多物种模型，该模型作为复杂环境中的生态和生物技术系统的统一框架（微生物群落、生物反应器等）。 该模型包含了由环境协变量调节的非局部种内和种间相互作用。 在对死亡率、繁殖率和相互作用核的一般假设下，我们建立了解的存在性、唯一性和正性。 我们沿着两条路线展示了该模型的实际相关性。 首先，多物种示例，特别是非传递性（循环）竞争模型，在该模型假设下，对单一物种施加的控制可以实现系统的全局稳定。 其次，疟疾媒介蚊子的种群动态，我们开发了两种控制策略（生物和遗传）。 在生物控制情景中，我们通过构建显式李雅普诺夫函数证明了水生区间的全局渐近稳定性。 数值模拟验证了理论结果，并比较了所提策略在减少载体密度和疟疾传播方面的有效性。