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Dynamics of the delay hematological cell model. (English) Zbl 1342.92068

Summary: In this paper, complex dynamics of a two-compartment model of production and regulation of the circulating blood neutrophil number are investigated. It is shown that the proliferative disorders may be possible due to factors of the apoptosis rate \(r_s\) of the haematopoietic stem cell and the cell cycle duration \(\tau_s\). Applying a recent geometrical criterion for the Hopf bifurcation and transient behaviors of delay systems to this model, we separate the stable regime from the unstable regime on the \(r_s - \tau_s\) plane. Numerically, regimes of patterned periodic oscillations with low periodicity in the number of circulating blood cells appear on the \(r_s - \tau_s\) plane. It is found that the dominated period-adding bifurcation mechanism leads transitions from period-\(n\) to period-\((n + 1)\), eventually changes to the complex attractor with high-periodicity or chaos.

MSC:

92C37 Cell biology
92C35 Physiological flow
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