TY - BOOK ID - 4864324 TI - Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays AU - Ahsen, Mehmet Eren. AU - Özbay, Hitay. AU - Niculescu, Silviu-Iulian. PY - 2015 SN - 9783319156064 3319156055 9783319156057 3319156063 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Mathematics. KW - Systems Theory, Control. KW - Mathematical and Computational Biology. KW - Gene Expression. KW - Control, Robotics, Mechatronics. KW - Gene expression. KW - Systems theory. KW - Mathématiques KW - Expression génique KW - Gene regulatory networks -- Mathematical models. KW - Gene regulatory networks. KW - Civil & Environmental Engineering KW - Engineering & Applied Sciences KW - Operations Research KW - Gene regulatory networks KW - Mathematical models. KW - System theory. KW - Biomathematics. KW - Control engineering. KW - Robotics. KW - Mechatronics. KW - Circuits, Gene KW - Gene circuits KW - Gene modules KW - Gene networks KW - Genetic regulatory networks KW - GRNs (Gene regulatory networks) KW - Modules, Gene KW - Networks, Gene regulatory KW - Networks, Transcriptional KW - Regulatory networks, Gene KW - Transcriptional networks KW - Genetic regulation KW - Nucleotide sequence KW - Genes KW - Expression KW - Mechanical engineering KW - Microelectronics KW - Microelectromechanical systems KW - Automation KW - Machine theory KW - Control engineering KW - Control equipment KW - Control theory KW - Engineering instruments KW - Programmable controllers KW - Biology KW - Mathematics KW - Systems, Theory of KW - Systems science KW - Science KW - Philosophy UR - https://www.unicat.be/uniCat?func=search&query=sysid:4864324 AB - This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. 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. 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. ER -