Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model
We analyze the asymptotic stability of a nonlinear system of two differential equations with delay,describing the dynamics of blood cell production. This process takes place in the bone marrow,where stem cells differentiate throughout division in blood cells. Taking into account an explicitrole of t...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2006-01-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.325 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590271766855680 |
|---|---|
| author | Fabien Crauste |
| author_facet | Fabien Crauste |
| author_sort | Fabien Crauste |
| collection | DOAJ |
| description | We analyze the asymptotic stability of a nonlinear system of two differential equations with delay,describing the dynamics of blood cell production. This process takes place in the bone marrow,where stem cells differentiate throughout division in blood cells. Taking into account an explicitrole of the total population of hematopoietic stem cells in the introduction of cells in cycle, weare led to study a characteristic equation with delay-dependent coefficients. We determine anecessary and sufficient condition for the global stability of the first steady state of our model,which describes the population's dying out, and we obtain the existence of a Hopf bifurcation forthe only nontrivial positive steady state, leading to the existence of periodic solutions. Theselatter are related to dynamical diseases affecting blood cells known for their cyclic nature. |
| format | Article |
| id | doaj-art-96ef6310492f4f9fb75ce70d7b8476a3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-96ef6310492f4f9fb75ce70d7b8476a32025-01-24T01:51:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-01-013232534610.3934/mbe.2006.3.325Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production ModelFabien Crauste0Laboratoire de Mathématiques Appliquées, FRE 2570, Université de Pau et des Pays de l'Adour, Avenue de l'université, 64000 PauWe analyze the asymptotic stability of a nonlinear system of two differential equations with delay,describing the dynamics of blood cell production. This process takes place in the bone marrow,where stem cells differentiate throughout division in blood cells. Taking into account an explicitrole of the total population of hematopoietic stem cells in the introduction of cells in cycle, weare led to study a characteristic equation with delay-dependent coefficients. We determine anecessary and sufficient condition for the global stability of the first steady state of our model,which describes the population's dying out, and we obtain the existence of a Hopf bifurcation forthe only nontrivial positive steady state, leading to the existence of periodic solutions. Theselatter are related to dynamical diseases affecting blood cells known for their cyclic nature.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.325blood cell modeldelay di?erential equationsstem cells.asymptotic stabilityhopf bifurcationdelay-dependent coe?cientscharacteristic equa-tion |
| spellingShingle | Fabien Crauste Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model Mathematical Biosciences and Engineering blood cell model delay di?erential equations stem cells. asymptotic stability hopf bifurcation delay-dependent coe?cients characteristic equa-tion |
| title | Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model |
| title_full | Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model |
| title_fullStr | Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model |
| title_full_unstemmed | Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model |
| title_short | Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model |
| title_sort | global asymptotic stability and hopf bifurcation for a blood cell production model |
| topic | blood cell model delay di?erential equations stem cells. asymptotic stability hopf bifurcation delay-dependent coe?cients characteristic equa-tion |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.325 |
| work_keys_str_mv | AT fabiencrauste globalasymptoticstabilityandhopfbifurcationforabloodcellproductionmodel |