Mathematical Sciences: Dynamical Systems in Structured Populations

数学科学：结构化总体中的动力系统

• 批准号: 9403884
• 负责人: Horst Thieme
• 金额: $ 9万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-15 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9403884&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Systems; Structured

9403884 Thieme The investigator studies the interplay of intrinsic population structures and population development via differential equations models. The structures of interest are induced by individual characteristics like (chronological or class) age, size, location etc. A particular goal is to identify those structures the introduction of which into a previously unstructured model changes the dynamical behavior of the model solutions. Specifically, he examines the influence of class age and chronological age on models of endemic diseases, the impact of body size structure on populations of zoo-plankton, and evolutionary aspects in structured metapopulation models. Mathematically, the introduction of population structure typically converts small systems of ordinary differential equations into large systems of ODEs or into integral, integro-differential, functional differential or partial differential equations. These equations are studied as evolution equations (dynamical systems) in an appropriate Banach space, which typically is infinite dimensional or has a large finite dimension. The study uses methods of linear and nonlinear functional analysis and dynamical systems theory. While establishing existence and uniqueness is a necessary and often not trivial step, the focus is on studying the qualitative behavior of solutions addressing stability, damped and undamped oscillations, persistence, and permanence. In order to interpret, forecast, manage and control the dynamics of microbial, plant, animal and human populations it is necessary to understand the interaction between inherent population structures (as given by age, body size, location etc.) and population development. The investigator develops mathematical concepts and tools to formulate and analyze appropriate models for this interdependence. Particular points of interests are how population structure affects stability, resilience, persistence and extinction of populations; fu rther, how to interpret population data in terms of individual well-being. The latter is relevant, e.g., for the use of micro-organisms in testing detergents. Important examples of structured populations are structured metapopulations. Many populations live in a patchy environment, leading to the formation of local populations that often go extinct and are recolonized by individuals immigrating from other local populations. The number of populations forming metapopulations of the above kind increases because the formerly continuous habitats of many species are fragmented. Metapopulation dynamics are important issues in conservation biology and re-establishment of naturally extinct species.

9403884 Thieme 研究人员通过微分方程模型研究内在种群结构和种群发展的相互作用。 感兴趣的结构是由个人特征（如（时间顺序或类别）年龄、大小、位置等）引起的。一个特定的目标是识别那些结构，将其引入到先前的非结构化模型中会改变模型解决方案的动态行为。 具体来说，他研究了班级年龄和实际年龄对地方病模型的影响、体型结构对浮游动物种群的影响以及结构化集合种群模型中的进化方面。 在数学上，总体结构的引入通常将小型常微分方程组转换为大型 ODE 系统或积分、积分微分、函数微分或偏微分方程。 这些方程在适当的 Banach 空间中作为演化方程（动力系统）进行研究，该空间通常是无限维或具有较大的有限维。 该研究采用线性和非线性泛函分析以及动力系统理论的方法。 虽然建立存在性和唯一性是一个必要且往往并非微不足道的步骤，但重点是研究解决稳定性、阻尼和无阻尼振荡、持久性和持久性的解决方案的定性行为。 为了解释、预测、管理和控制微生物、植物、动物和人类种群的动态，有必要了解固有种群结构（由年龄、体型、位置等给出）与种群发展之间的相互作用。 研究人员开发数学概念和工具来制定和分析这种相互依赖性的适当模型。 特别感兴趣的是人口结构如何影响人口的稳定性、复原力、持久性和灭绝；此外，如何从个人福祉角度解释人口数据。 后者是相关的，例如，与在测试洗涤剂中使用微生物有关。 结构化群体的重要例子是结构化元群体。 许多人口生活在不完整的环境中，导致当地人口的形成，这些当地人口往往灭绝并被从其他当地人口移民过来的个体重新殖民。 由于许多物种以前连续的栖息地被破碎，形成上述类型集合种群的种群数量增加。 种群动态是保护生物学和自然灭绝物种重建的重要问题。