Mathematical Sciences: Boundary Layer Phenomena for Nonlinear Functional Differential Equations

本计画将研究微分延迟方程与非扩张映射的迭代。主要的重点将放在扩展现有知识的情况下，几个延误和延误取决于国家。特别是对于依赖于小参数和依赖于状态的延迟的方程，该项目将研究当参数趋于零时产生周期解的边界层现象。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激发了要研究的主要问题。这些问题的普遍性将使结果与基础科学的大多数领域相关。

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.