Jose Louis Avila Alonso, C. Bonnet, E. Fridman, F. Mazenc, J. Clairambault
{"title":"Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia","authors":"Jose Louis Avila Alonso, C. Bonnet, E. Fridman, F. Mazenc, J. Clairambault","doi":"10.1109/CDC.2014.7039860","DOIUrl":null,"url":null,"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.","PeriodicalId":202708,"journal":{"name":"53rd IEEE Conference on Decision and Control","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"53rd IEEE Conference on Decision and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2014.7039860","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
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.
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