Periodic Oscillation in Neutrophil Models with Time Delays

To understand dynamical characters of neutrophil dynamical behavior, the sensitivity of delay factors which has effects on system dynamic behavior is ubiquitous due to system’s highly nonlinearity. Here we prove that delay supports a subcritical Hopf bifurcation, underlying a feedback mechanism during stem cells proliferation process while changing its coefficient of amplification. The given cell model reproduces a bistable dynamic regime of blood cells and hysteresis. Applying multiple scale method, oscillation motion near Hopf point is discussed. The stability limit of steady state to be abruptly periodic solution is detected.