Browsing by Subject "Global stability"

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    Stability analysis of a dynamical model representing gene regulatory networks
    (2012) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. I.
    In this paper we perform stability analysis of a class of cyclic biological processes involving time delayed feedback. More precisely, we analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. We derive a set of conditions implying global stability of the genetic regulatory network under positive feedback. As a special case, we also consider homogenous genetic regulatory networks and obtain an appropriate stability condition which depends only on the parameters of the nonlinearity function. © 2012 IFAC.
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    Stability analysis of cell dynamics in leukemia
    (E D P Sciences, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun, H.; Clairambault, J.
    In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.