All Issues

Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Neimark-Sacker bifurcation of a semi-discrete hematopoiesis model
Keywords:Semi-discrete blood cell production model, Neimark-Sacker b- ifurcation, 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 [20, 21]. 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.