Title :
Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia
Author :
Avila, J.L. ; Bonnet, C. ; Fridman, E. ; Mazenc, F. ; Clairambault, J.
Author_Institution :
Equipe DISCO, Inria, Gif-sur-Yvette, France
Abstract :
In this paper we perform a stability analysis of two systems of partial differential equations (PDEs) modelling cell dynamics in Acute Myeloid Leukemia. By using a Lyapunov approach, for an equilibrium point of interest, we obtain stability bounds depending on the parameters of the systems. First, we derive sufficient conditions for boundedness of solutions. Then, asymptotic stability conditions are obtained. The results are illustrated with numerical examples and simulations.
Keywords :
Lyapunov methods; asymptotic stability; blood; cancer; cellular biophysics; partial differential equations; Lyapunov approach; PDE; acute myeloid leukemia; asymptotic stability conditions; cell dynamics modelling; partial differential equations; solution boundedness; stability analysis; stability bounds; sufficient conditions; Analytical models; Cancer; Mathematical model; Sociology; Stability analysis; Statistics; Trajectory;
Conference_Titel :
Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on
Conference_Location :
Los Angeles, CA
Print_ISBN :
978-1-4799-7746-8
DOI :
10.1109/CDC.2014.7039860
