Anael Verdugo

Dynamics of Gene Networks with Time Delays: Numerical Studies for Differential Delay Equations Anael Verdugo

Over the past few decades, mathematical modeling has been extensively used to understand biological phenomena. From a cellular biology viewpoint, there has been much evidence that biochemical processes depend not only on the present state of the cell but also on previous reactions. The effects of these previous reactions are commonly due to a characteristic time delay between the signal and the response of the system. From a mathematical viewpoint, time delays bring complexity into the study of biological systems, but due to recent advances in the fields of differential delay equations and dynamical systems theory, these problems are now more tractable. The main purpose of this book is to provide a friendly mathematical approach to the analysis of differential delay equations. The analyses presented in this work should help modelers in the field of cell biology to further their understanding of some of the mathematical methods currently used to study gene networks with time delays.