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Stability analysis of PDE’s modelling cell dynamics in Acute Myeloid Leukemia

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Abstract

In this paper we perform a stability analysis oftwo systems of partial differential equations (PDEs) modellingcell dynamics in Acute Myeloid Leukemia. By using a Lyapunovapproach, for an equilibrium point of interest, we obtain stabilitybounds depending on the parameters of the systems. First,we derive sufficient conditions for boundedness of solutions.Then, asymptotic stability conditions are obtained. The resultsare illustrated with numerical examples and simulations.
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Dates and versions

hal-01110304 , version 1 (27-01-2015)

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Jose Luis Avila Alonso, Catherine Bonnet, Emilia Fridman, Frédéric Mazenc, Jean Clairambault. Stability analysis of PDE’s modelling cell dynamics in Acute Myeloid Leukemia. 53rd IEEE Annual Conference on Decision and Control (CDC 2014), Dec 2014, Los Angeles, United States. ⟨10.1109/cdc.2014.7039860⟩. ⟨hal-01110304⟩
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