Mathematical Sciences: Boundary Layer Phenomena for Nonlinear Functional Differential Equations

这个项目将研究微分时滞方程和非扩张映射的迭代。主要重点将放在将现有知识推广到几次延误和延误的情况，视情况而定。特别是，对于依赖于小参数的方程和依赖于状态的延迟，该项目将研究当参数趋于零时导致周期解的边界层现象。我们将通过推广线性随机矩阵的性质来分析非扩张映射。生物学、经济学、物理学甚至其他数学分支中的模型都激励着要研究的主要问题。这些问题的普遍性将使结果与大多数基础科学领域相关。

This project will study differential delay equations and iterations of nonexpansive maps. Main emphasis will be placed in extending current knowledge to the cases of several delays and of delays depending on the state. In particular, for equations depending on a small parameter and delays depending on the state, the project will study the boundary layer phenomenon resulting in periodic solutions when the parameter tends to zero. Analysis of nonexpansive mappings through generalizations of properties of linear stochastic matrices will be pursued. Models in biology, economics, physics and even other branches of mathematics motivate the main problems to be studied. The generality of the questions will make the results relevant to most areas of basic science.