Mathematical Sciences: Stable and Chaotic Behavior of Deterministic Models of Interacting Populations with/withoutGenetic Variation

研究人员研究了系统的动力学行为 描述相互作用的差分和微分方程 有和没有遗传变异的人群。 特别 将考虑到混乱和奇怪的开始， 吸引子，例如，一个倍周期级联到一个奇怪的 吸引子，通过改变一个单一的种内 参数. 提案者将试图扭转 周期性的收获或播种造成的混乱。 这些研究将包括数值实验和分析 使用稳定性理论等技术的论点， 不变集理论、分歧和扰动理论。 生态系统的发展，无论是自然的还是管理的， 受到环境和环境之间复杂相互作用的影响， 遗传成分。 该研究将研究 数学模型试图捕捉一些基本的 这些互动的特点。 研究的目标 包括了解：（一）环境和遗传 参数影响物种共存和灭绝;（ii） 生态系统密度混沌波动的开始 人口;以及（iii）如何收获和播种战略 影响生态系统的稳定性。 这些知识可能有助于维持生物多样性， 自然生态系统，在管理自然资源， 如森林和湖泊，以及抗病植物的发展 作物

The investigators study the dynamical behavior of systems of difference and differential equations that describe interacting populations with and without genetic variation. Special consideration will be given to the onset of chaos and of strange attractors, e.g., a period-doubling cascade to a strange attractor that is forced by changing a single intraspecific parameter. The proposers will attempt to reverse the onset of chaos by the periodic harvesting or seeding of a population. These studies will include numerical experiments and analytical arguments employing techniques such as stability theory, invariant set theory, bifurcation and perturbation theory. The development of an ecosystem, whether natural or managed, is affected by complex interactions among environmental and genetic components. The proposed research will study mathematical models that attempt to capture some of the essential features of these interactions. The objectives of the research include understanding: (i) how environmental and genetic parameters influence species coexistence and extinction; (ii) the onset of chaotic fluctuations in the densities of ecosystem populations; and (iii) how harvesting and seeding strategies affect ecosystem stability. Such knowledge may help in maintaining biodiversity in natural ecosystems, in the management of natural resources such as forests and lakes, and in the development of disease-resistant crops.