LOCAL AND GLOBAL HOPF BIFURCATIONS IN A DELAYED HUMAN RESPIRATORY SYSTEM

摘要

This paper considers a delayed human respiratory model. Firstly, the stability of the equilibrium of the model is investigated and the occurrence of a sequence of Hopf bifurcations of the model is proved. Secondly, the explicit algorithms which determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by applying the normal form method and the center manifold theory. Finally, the existence of the global periodic solutions is showed under some assumptions on the model.