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Hitay Özbay’s New Book

Associate Provost Hitay Özbay of the Department of Electrical and Electronics Engineering has coauthored a new book with Mehmet Eren Ahsen and Silviu-lulian Niculescu. The 94-page volume, “Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays,” has been published by Birkhäuser Basel as part of the series “Springer Briefs in Control, Automation and Robotics.”

The book examines a deterministic, ODE-based model for gene regulatory networks (GRNs) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides a concise introduction to molecular biology and GRNs for mathematicians. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives.

One chapter is devoted to the analysis of GRNs under negative feedback with time delays, and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. The book also contains exercises to allow its use in graduate-level courses.

Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.