Periodical Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model with Feedback Control ()
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.
Share and Cite:
Ma, S. (2023) Periodical Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model with Feedback Control.
International Journal of Modern Nonlinear Theory and Application,
12, 18-29. doi:
10.4236/ijmnta.2023.121002.
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