Stability analysis of cell dynamics in leukemia
Mathematical Modelling of Natural Phenomena
E D P Sciences
203 - 234
Item Usage Stats
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.
Local asymptotic stability
Nonlinear small gain
Published Version (Please cite this version)http://dx.doi.org/10.1051/mmnp/20127109
Showing items related by title, author, creator and subject.
Ahsen, M. E.; Özbay, Hitay; Niculescu, S. I. (2012)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 ...
Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay (Elsevier, 2013)This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple ...
Ünyelioğlu, Konur Alp; Özgüler, Arif Bülent (Taylor & Francis, 1992)Electrical and The decentralized stabilization problem of multivariable finite-dimensional systems is considered in a fractional set-up. A new synthesis procedure for decentralized stabilizing compensators is proposed. The ...