Abstract
In this chapter of the book, a dynamical model of the gene regulatory networks (GRNs) under positive feedback is analyzed. The model considered involve static nonlinearities with negative Schwarzian derivatives, and a time delay in the feedback path. A set of conditions are derived for the global stability of the class of GRNs considered. As a special case, homogenous GRNs are also analyzed and an appropriate stability condition is obtained; that depends only on the parameters of the nonlinearity function, which is assumed to be a Hill type function. In particular, conditions leading to bistability of the system are obtained. The results presented here naturally extend to similar classes of cyclic biological processes involving time delayed feedback.
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Ahsen, M.E., Özbay, H., Niculescu, SI. (2014). Analysis of Gene Regulatory Networks under Positive Feedback. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_10
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DOI: https://doi.org/10.1007/978-3-319-01695-5_10
Publisher Name: Springer, Cham
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