Browsing by Author "Ahsen, M. E."

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Open Access
Analysis of a gene regulatory network model with time delay using the secant condition
(IEEE, 2016-10-04) Ahsen, M. E.; Özbay, Hitay; Nicolescu, Silviu-Iulian
A cyclic model for gene regulatory networks with time delayed negative feedback is analyzed using an extension of the so-called secant condition, which is originally developed for systems without time delays. It is shown that suf cient conditions obtained earlier for delay-independent local stability can be further improved for homogenous networks to obtain delay-dependent necessary and suf cient conditions, which are expressed in terms of the parameters of the Hill-type nonlinearity.
Open Access
Analysis of deterministic cyclic gene regulatory network models with delays
(Springer Publishing Company, 2015) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. -I.
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.
Open Access
On the analysis of a dynamical model representing gene regulatory networks under negative feedback
(Wiley, 2014-07-25) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. I.
In this work, stability analysis is performed for a cyclic dynamical model of gene regulatory networks involving time delays, under negative feedback. The model considered has nonlinearities with negative Schwarzian derivatives. Sufficient conditions implying global stability of these types of GRNs are obtained. The special case of homogenous gene regulatory networks is also studied; in this case, the proposed stability conditions depend only on the parameters of the nonlinearity function. Illustrative numerical examples complete the presentation.
Open Access
Preface
(Springer Publishing Company, 2015) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. I.
[No abstract available]
Open Access
A secant condition for cyclic systems with time delays and its application to Gene Regulatory Networks
(IFAC, 2015) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. -I.
A stability condition is derived for cyclic systems with time delayed negative feedback. The result is an extension of the so-called secant condition, which is originally developed for systems without time delays. This extension of the secant condition gives a new local stability condition for a model of GRNs (Gene Regulatory Networks) under negative feedback. Stability robustness of homogenous networks is also investigated.
Open Access
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.