Alaoui, T.H., Yafia, R. and Aziz-Alaoui, M.A. (2007) Hopf Bifurcation Direction in a Delayed Hematopoietic Stem Cells Model. Arab Journal of Mathematics and Mathematical Sciences, 1, 35-50.

has been cited by the following article:

• TITLE: Bifurcation Analysis of a Neutrophil Periodic Oscillation Model with State Feedback Control

  AUTHORS: Suqi Ma

  KEYWORDS: Neutrophil Phase, Time Delay, Hopf Bifurcation, DDE-Biftool, Fold Periodical Bifurcation, Period-Doubling Bifurcation

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.12 No.1, March 23, 2023

  ABSTRACT: The mathematical model of stem cells is discussed with its motivation to describe the tissue relationship by technically introducing a two compartments model. The clear link between the proliferation phase of stem cells and the circulating neutrophil phase is set forth after delay feedback control of the state variable of stem cells. Hopf bifurcation is discussed with varying free parameters and time delays. Based on the center manifold theory, the normal form near the critical point is computed and the stability of bifurcating periodical solution is rigorously discussed. With the aids of the artificial tool on-hand which implies how much tedious work doing by DDE-Biftool software, the bifurcating periodic solution after Hopf point is continued by varying time delay.