| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014
Issue dedicated to Michael Mackey
|
|
|---|---|---|
| Page(s) | 58 - 78 | |
| DOI | https://doi.org/10.1051/mmnp/20149105 | |
| Published online | 07 February 2014 | |
Existence and Stability of Limit Cycles in a Two-delays Model of Hematopoiesis Including Asymmetric Division
“POLITEHNICA” University of Bucharest, Department of
Mathematics and Informatics, Splaiul Independentei 313
RO-060042
Bucharest,
Romania
⋆
Corresponding author. E-mail: halanay@mathem.pub.ro
A two dimensional two-delays differential system modeling the dynamics of stem-like cells and white-blood cells in Chronic Myelogenous Leukemia is considered. All three types of stem cell division (asymmetric division, symmetric renewal and symmetric differentiation) are present in the model. Stability of equilibria is investigated and emergence of periodic solutions of limit cycle type, as a result of a Hopf bifurcation, is eventually shown. The stability of these limit cycles is studied using the first Lyapunov coefficient.
Mathematics Subject Classification: 34K18 / 34K20 / 92D25
Key words: leukemia / asymmetric division / stability / Hopf bifurcation / limit cycle
© EDP Sciences, 2014
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