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.
