Title: From Age-Structured Trophic Networks to Applied Control : Stabilization and Harvesting Strategies for Non-Transitive Competition and the Dynamics of Mosquitoes Show Chinese title

Title: 从年龄结构营养网络到应用控制：非传递竞争的稳定化和捕捞策略以及蚊子的动力学

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, etc.). 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: (i) 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; furthermore, verification of the Kalman condition in this context provides an essential theoretical prerequisite and highlights that this single control acts indirectly on all other species; and (ii) the population dynamics of malaria-vector mosquitoes, for which we develop two control strategies (biological and genetic) and, in the biological-control scenario, 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的年龄结构多物种模型，该模型作为复杂环境（微生物群落、生物反应器等）中生态和生物技术系统的统一框架。 该模型的构建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。 我们沿着两个方面说明了该模型的实际相关性：(i) 多物种示例，特别是非传递性（循环）竞争模型，在此模型假设下，对单一物种施加的控制可以实现系统的全局稳定；此外，在这种情况下验证卡尔曼条件提供了必要的理论前提，并突显出这种单一控制间接作用于所有其他物种；以及 (ii) 疟疾媒介蚊子的种群动态，我们为此开发了两种控制策略（生物和遗传），在生物控制情景中，通过构建一个显式李雅普诺夫函数证明了水生部分的全局渐近稳定性。 数值模拟验证了理论结果，并比较了所提出的策略在减少载体密度和疟疾传播方面的有效性。