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.