DYNAMICS OF GENE NETWORKS WITH TIME DELAYS

The study of time delays and their influence on gene network dynamics is the central topic of this thesis. Three different gene models with delay are stud-ied: (1) a single gene-mRNA-protein model (2) a multiple gene network model (3) a continuous gene network model Chapters 2 and 3 present a brief introduction to the fields of gene regulatory networks and delay differential equations, respectively. Previous results rele-vant for this thesis are presented and a friendly overview with figures and ex-amples is given. The purpose of these two chapters is to present a self-contained introduction of the main ideas to the rest of the thesis. Chapter 4 presents a linear andnonlinear analysis of (1) a single gene-mRNA-protein system given by M ̇ = αm