Özbay, HitayBonnet, C.Benjelloun, H.Clairambault, J.2016-02-082016-02-0820120973-5348http://hdl.handle.net/11693/21590In 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.EnglishAbsolute stabilityAcute leukemiaDistributed delaysGlobal stabilityAbsolute stabilityAcute leukemiaCell dynamicsDistributed delaysGlobal stabilityLinearized systemsLocal asymptotic stabilityNonlinear small gainNumerical examplePositive equilibriumStability analysisStability conditionSub-systemsSystem modelingAsymptotic stabilityDiseasesDynamicsNonlinear feedbackStability criteriaSystem stabilityArticle10.1051/mmnp/20127109