Formulation and Analysis of Nonlinear Mathematical Models with Applications to Population Dynamics

非线性数学模型的制定和分析及其在人口动态中的应用

• 批准号: RGPIN-2016-05769
• 负责人: Wolkowicz, Gail
• 金额: $ 1.97万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635717
• 关键词: Formulation; Analysis; Nonlinear; Mathematical; Models

My research focuses on developing and analyzing mathematical models to study population dynamics. I am interested in how model assumptions influence the predictions, especially the entire range of possible dynamics. Many processes involve time delays that are ignored in models for mathematical tractability. I have been investigating the consequences of ignoring these delays as well as how the delays are modeled, i.e., using different distributions. Many mathematical functions used in models are not mechanistically justified, but rather only their basic form is suggested from data. I have been investigating the implications of using different choices for the mathematical forms (with the same properties) on model predictions. Is one form more likely to predict extinction of species than another? Is one form more likely to predict that a population size oscillates as opposed to approaching a constant population size? Is this influence consistent or model dependent?

我的研究重点是开发和分析数学模型来研究人口动态。我感兴趣的是模型假设如何影响预测，特别是整个可能的动态范围。许多过程涉及在数学易处理性模型中被忽略的时间延迟。我一直在研究忽略这些延迟的后果以及如何对延迟进行建模，即，使用不同的分布。模型中使用的许多数学函数并没有机械地证明是合理的，而是从数据中提出了它们的基本形式。我一直在研究对模型预测的数学形式（具有相同属性）使用不同选择的含义。一种形式比另一种形式更有可能预测物种灭绝吗？是否有一种形式更有可能预测人口规模的振荡，而不是接近恒定的人口规模？这种影响是一致的还是依赖于模型的？