Abstract
The dynamics of a system composed of hematopoietic stem cells and its relationship with neutrophils is ubiquitous due to periodic oscillating behavior induce cyclical neutropenia. Underlying the methodology of state feedback control with two time delays, double Hopf bifurcation occurs as varying time delay to reach its threshold value. By applying center manifold theory, the analytical analysis of system exposed the different dynamical feature in the classified regimes near double Hopf point. The novel dynamics as periodical solution and quasi-periodical attractor coexistence phenomena are explored and verified by numerical simulation.
Highlights
And Biologically, the discussion of the complex dynamics of hematopoietic cell model is ubiquitous and interesting due to its inherent highly nonlinear attribute
The dynamics of a system composed of hematopoietic stem cells and its relationship with neutrophils is ubiquitous due to periodic oscillating behavior induce cyclical neutropenia
A blood cell model which composed of two compartment cells known as hematopoietic stem cells and its relationship with neutrophil was investigated
Summary
And Biologically, the discussion of the complex dynamics of hematopoietic cell model is ubiquitous and interesting due to its inherent highly nonlinear attribute. Mackeys model proposed at the end of the seventies describe a decoupled quiescent phase of HSCS to study the dynamics of HSCs and its related diseases (Mackey, 1978) Since it has been improved and analyzed by many authors, including Mackey and coauthors (Pujo−Menjouet & Mackey, 2004; Pujo−Menjouet et al, 2005; Fowler & Mackey, 2002). The delay in circulating neutrophil is τN which can be decomposed as different time period experienced, that is, the proliferation time τNP (days) of its progenitor cells and the maturation time τNM (days) of cyclical neutropenia. Numerical simulation further verifies the classified dynamical results, and coexistence of periodical solutions and torus are detected near double Hopf bifurcation point
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