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Neimark-Sacker bifurcation of a semi-discrete hematopoiesis model
Keywords:Semi-discrete blood cell production model, Neimark-Sacker bifurcation, invariant closed curve, center manifold theorem, normal form method.
      In this paper, we derive a semi-discrete system for a nonlinear model of blood cell production. The local stability of its fixed points is investigated by employing a key lemma from [23, 22]. It is shown that the system can undergo Neimark-Sacker bifurcation. By using the Center Manifold Theorem, bifurcation theory and normal form method, the conditions for the occurrence of Neimark-Sacker bifurcation and the stability of invariant closed curves bifurcated are also derived. The numerical simulations verify our theoretical analysis and exhibit more complex dynamics of this system.