Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics

Nonlinear Analysis: Real World Applications

Volumn 6, Issue 4, 2005, Pages 651-670

  Adimy, Mostafa ^a   Crauste, Fabien ^a   Ruan, Shigui ^b  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b Department of Biology   (United States)

Author keywords

Blood production system; Delay differential equations; Hopf bifurcation; Stability; Stem cells

Indexed keywords

BIFURCATION (MATHEMATICS); BLOOD; CELLS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; THEOREM PROVING;

BLOOD PRODUCTION SYSTEM; DELAY DIFFERENTIAL EQUATIONS; HOPF BIFURCATION; STEM CELLS;

MATHEMATICAL MODELS;

EID: 15844377066     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2004.12.010     Document Type: Article

References (16)

1. M. Adimy, F. Crauste, Global stability of a partial differential equation with distributed delay due to cellular replication, Nonlinear Anal. 54 (8) (2003) 1469-1491.
2. J. Bélair, M.C. Mackey, J.M. Mahaffy, Age-structured and two-delay models for erythropoiesis, Math. Biosci. 128 (1995) 317-346.
3. G. Bradford, B. Williams, R. Rossi, I. Bertoncello, Quiescence, cycling, and turnover in the primitive haematopoietic stem cell compartment, Exper. Hematol. 25 (1997) 445-453.
4. 0 phase in the cell cycle, Cell. Tissue Kinet. 19 (1970) 321-334.
5. J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1960.
6. A.C. Fowler, M.C. Mackey, Relaxation oscillations in a class of delay differential equations, SIAM J. Appl. Math. 63 (2002) 299-323.
7. J.K. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences, vol. 99, Springer, New York, 1993.
8. C. Haurie, D.C. Dale, M.C. Mackey, Cyclical neutropenia and other periodic hematological diseases: A review of mechanisms and mathematical models, Blood 92 (1998) 2629-2640.
9. M.C. Mackey, A unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis, Blood 51 (1978) 941-956.
10. M.C. Mackey, Dynamic hematological disorders of stem cell origin, in: J.G. Vassileva-Popova, E.V. Jensen, (Eds.), Biophysical and Biochemical Information Transfer in Recognition, Plenum, New York, 1979, pp. 373-409.
11. M.C. Mackey, Cell kinetic status of haematopoietic stem cells, Cell Prolif. 34 (2001) 71-83.
12. M.C. Mackey, C. Haurie, J. Bélair, Cell replication and control, in: A. Beuter, L. Glass, M.C. Mackey, M.S. Titcombe, (Eds.) Nonlinear Dynamics in Physiology and Medicine, Springer, New York, 2003, pp. 233-269.
13. J.M. Mahaffy, J. Bélair, M.C. Mackey, Hematopoietic model with moving boundary condition and state dependent delay, J. Theor. Biol. 190 (1998) 135-146.
14. 0 model of hematopoietic stem cells, SIAM J. Appl. Dynam. Sys.; in press.
15. L. Pujo-Menjouet, M.C. Mackey, Contribution to the study of periodic chronic myelogenous leukomia, Comptes Rendus Biol. 327 (2004) 235-244.
16. L. Sachsm, The molecular control of hemopoiesis and leukemia, C. R. Acad. Sci. Paris 316 (1993) 882-891.