Abstract
The hematological stem cells model is introduced with neutrophil dynamics of two department model setting forth. During the cells differentiation and proliferation process, the neutrophils are functioned with negative feedback with delay history, which contains delayed amplification coefficient. In more general view, the new introduction rate is given to replace the familiar Hill function which is helpful to understand the complex dynamics of neutrophils. The double Hopf bifurcation is calculated with the artificial handtools named DDE-Biftool, which is observed as the self-intersection of Hopf lines. The continuation of periodical solutions arising from Hopf points are done and the longer period solutions are manifested with multi-rhythm and bursting oscillation. The near dynamics of double Hopf points is simulated by DDE-Biftool with different route design, the multi-period attractors, quasi-periodical solutions and chaos are observed.
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