Local Asymptotic Stability Conditions for the Positive Equilibrium of a System Modeling Cell Dynamics in Leukemia

Hitay Ozbay (1) , Catherine Bonnet (2, 3) , Houda Benjelloun (3) , Jean Clairambault (4, 5)

1 Department of Electrical and Electronics Engineering
2 L2S - Laboratoire des signaux et systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 LJLL - Laboratoire Jacques-Louis Lions
5 BANG - Nonlinear Analysis for Biology and Geophysical flows

A distributed delay system with static nonlinearity has been considered in the literature to study the cell dynamics in leukemia. In this chapter local asymptotic stability conditions are derived for the positive equilibrium point of this nonlinear system. The stability conditions are expressed in terms of inequalities involving parameters of the system. These inequality conditions give guidelines for development of therapeutic actions.

Domaines: Automatique

Hitay Ozbay, Catherine Bonnet, Houda Benjelloun, Jean Clairambault. Local Asymptotic Stability Conditions for the Positive Equilibrium of a System Modeling Cell Dynamics in Leukemia. R. Sipahi and T. Vyhlidal and S-I. Niculescu and P. Pepe. Time Delay Systems: Methods, Applications and New Trends, 423, Springer, pp.187-197, 2012, LNCIS, 978-3-642-25221-1. ⟨10.1007/978-3-642-25221-1_14⟩. ⟨hal-00780527⟩