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

Mostafa Adimy (1, 2) , Fabien Crauste , Shigui Ruan (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics
3 Department of Mathematics [Miami]

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell cycle duration and is uniformly distributed on an interval. We obtain stability conditions independent of the delay. We also show that the distributed delay can destabilize the entire system. In particularly, it is shown that Hopf bifurcations can occur.

Mots clés: blood production system; stem cells; delay differential equations; stability; Hopf bifurcation

Domaines: Equations aux dérivées partielles [math.AP]

Mostafa Adimy, Fabien Crauste, Shigui Ruan. Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics. Nonlinear Analysis: Real World Applications, 2005, 6 (4), pp.651-670. ⟨10.1016/j.nonrwa.2004.12.010⟩. ⟨hal-00375966⟩