Mathematical Sciences: Boundary Layer Phenomena for Functional Differential Equations and Means and Their Iterations

该项目继续研究数学理论， 泛函微分方程 特别感兴趣的是 这些方程涉及时间延迟和存在一个 负反馈条件 奇异摄动方法将 被雇用。 这种类型的方程出现在许多 应用如光学、生理学和数学生物学。 在这些方程方面已经取得了相当大的进展。 重点将放在了解的动态 在一个区间内给出规定值的解。 一 一个特殊的例子是， 缓慢变化的解决方案。 其他工作将集中在方程 其中具有依赖于状态的时间滞后， 细胞生产和农业商品周期。 在这里， 人们寻找解的周期性， 深入了解解的渐近性质， 扰动参数趋于零。 另一类需要考虑的问题包括 泛函微分方程 取决于解的延迟值以及 当前值。这里的主要目标是确定是否存在 没有周期等于4的非常数解。 示例 这表明这个猜想是正确的，尽管它的有效性是 这一点也不确定

This project continues work on the mathematical theory of functional differential equations. Of particular interest are those equations involving time delay and the presence of a negative feed-back condition. Singular perturbation methods will be employed. Equations of this type arise in a number of applications such as optics, physiology and mathematical biology. Considerable progress has been made on these equations. Emphasis will be placed on understanding the dynamics of solutions having prescribed values given over an interval. A particular instance would be to give conditions for the existence of slowly varying solutions. Other work will focus on equations where one has state dependent time lags which model blood cell production and agricultural commodity cycles. Here again, one looks for periodicity properties of solutions as well as insight into the asymptotic properties of solutions as the perturbation parameter tends to zero. Another class of problems to be considered involves functional differential equations where the forcing functional depends on the delayed values of the solution as well as the current values. Here the primary object is to determine if there are no nonconstant solutions of period equal to four. Examples indicate that this conjecture is true, although its validity is by no means assured.