Mathematical Sciences: Modeling Cellular Control Systems

这项研究将继续研究细胞 控制系统和延迟微分方程。 有 三大研究领域。 第一个领域是 与J. W.博士合作进行跨学科研究。 Zyskind关于复制起始的建模， 大肠杆菌，数学模型的开发，以帮助我们 理解DNA起始的实验观察 复制的 第二个项目使用分析和数值 研究大小和区室化对 具有扩散和扩散的细胞控制模型的稳定性 延误了. 动态增长模型的开发和比较， 实验数据 第三个领域探讨了一个 双时滞线性微分方程 数值方法 分叉表面被发现，和方法 将它们的几何形状与分析 结果 前两个项目将数学研究与 目前的生物问题。 这三个问题都需要 开发新的分析技术，可应用于 许多建模问题。

This investigation will continue the study of cellular control systems and delay differential equations. There are three main areas of study. The first area is an interdisciplinary study done in collaboration with Dr. J. W. Zyskind on the modeling of initiation of replication in Escherichia coli, Mathematical models are developed to aid in our understanding of experimental observations on initiation of DNA replication. The second project uses analytical and numerical methods to study the effects of size and compartmentalization on the stability of cellular control models with diffusion and delays. Dynamic growth models are developed and compared to experimental data. The third area explores the stability of a linear differential equation with two delays using analytical and numerical methods. Bifurcation surfaces are found, and methods are investigated to connect their geometries to analytical results. The first two projects link mathematical studies to current biological problems. All three problems require the development of new techniques of analysis that can be applied to many modeling problems.