Mathematical Sciences: Boundary Layer Phenomena for Nonlinear Functional Differential Equations

本项目将研究微分延迟方程和 非扩张映射的迭代 重点将放在 在扩展现有知识的情况下，几个延误， 延迟取决于国家。 特别是，对于方程 取决于小参数和取决于状态的延迟， 该项目将研究边界层现象， 当参数趋于零时的周期解。 分析 的性质的推广 将追求线性随机矩阵。 生物学、经济学、物理学甚至其他领域的模型 数学的分支激发了要研究的主要问题。 问题的普遍性将使结果与以下方面相关： 大部分基础科学领域。

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.