Existence and Stability of Limit Cycles in a Two-delays Model of Hematopoiesis Including Asymmetric Division

摘要

A two dimensional two-delays differential system modeling the dynamics of stemlike 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.