Mathematical Sciences: Biological Models with Time Delays and Spatial Dependence

本研究将继续研究细胞控制模型。这个项目有三个主要的研究领域。首先，首席研究员将扩展他对包括时间延迟和空间效应的隔间模型的分析。研究这些模型是为了证明描述生物系统的微分方程的稳定性。研究的第二个领域详细介绍了大肠杆菌中OriC开始复制的模型。该模型基于生物化学动力学，正在与正在进行的实验一起开发。最后一个问题是检验一个有两个时滞的线性时滞微分方程。对于固定时滞，用系数参数检验了分岔面。对于这三个问题，该项目将适用于在建模某些生物和物理现象时出现的广泛类别的方程。

This investigation will continue the study of cellular control models. There are three main areas of study in this project. First, the principal investigator will extend his analysis of compartmental models which include both time delays and spatial effects. These models are studied to show the stability of the differential equations describing the biological system. The second area of study details a model for the initiation of replication at OriC in E. coli. The model, which is based on biochemical kinetics, is being developed in conjunction with ongoing experiments. The final problem is to examine a linear delay differential equation with two time delays. For fixed delays the bifurcation surface is examined with respect to the coefficient parameters. For all three problems the project will be applicable to broad classes of equations that occur in modeling certain biological and physical phenomena.