Article citationsMore>>

Mackey, M.C., Pujo-Menjouet, L. and Wu, J. (2006) Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia. SIAM Journal on Mathematical Analysis, 38, 166-187.
https://doi.org/10.1137/04061578X

has been cited by the following article:

• TITLE: Periodical Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model with Feedback Control

  AUTHORS: Suqi Ma

  KEYWORDS: Bifurcation, Saddle-Node Bifurcation, Period-Doubling Bifurcation, Hopf Bifurcation, Time Delay

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

  ABSTRACT: The delay feedback control brings forth interesting periodical oscillation bifurcation phenomena which reflect in Mackey-Glass white blood cell model. Hopf bifurcation is analyzed and the transversal condition of Hopf bifurcation is given. Both the period-doubling bifurcation and saddle-node bifurcation of periodical solutions are computed since the observed floquet multiplier overpass the unit circle by DDE-Biftool software in Matlab. The continuation of saddle-node bifurcation line or period-doubling curve is carried out as varying free parameters and time delays. Two different transition modes of saddle-node bifurcation are discovered which is verified by numerical simulation work with aids of DDE-Biftool.