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

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。许多过程涉及时间延迟，在数学可追溯性模型中被忽略。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不是机械地证明的，而只是从数据中提出它们的基本形式。我一直在研究在模型预测中使用不同选择的数学形式（具有相同属性）的含义。一种形式比另一种形式更有可能预示物种灭绝吗？是否有一种形式更有可能预测种群规模的波动而不是接近恒定的种群规模？这种影响是一致的还是依赖于模型的？

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?