Titlebook: Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays; Mehmet Eren Ahsen,Hitay ?zbay,Silviu-Iulian Nicule Book 2015

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Functions with Negative Schwarzian Derivatives,This chapter is devoted to the analysis on functions with NSD (negative Schwarzian derivatives). First, basic properties of functions with NSD are given and a classification result is proven for such functions. Then, an analysis is made on the fixed points for functions with NSD.

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Summary and Concluding Remarks,In this chapter, the analysis results for GRNs under negative and positive feedback are discussed and concluding remarks are made. Some possible future research directions are also pointed out.

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Book 2015n 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 dela

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Time Zone Differences and Service Tradee. Then, delay independent global stability, and instability, conditions are derived. For a delay dependent stability condition the secant condition is extended to cover systems with time delays. Special stability conditions are derived for homogenous GRNs where nonlinearities are Hill functions.

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