Hopf Bifurcation Analysis, With Time Delay Of The Human Respiratory System

This paper considers the local and global Hopf bifurcations of the human respi-ratory system,using Hopf bifurcation theorems.Firstly, the stability of the equilibriumof the system is investigated and the occurrence of the local Hopf bifurcations of thesystem is proved.Secondly, using the normal form method and the center manifold the-ory, the explicit algorithms which determine the direction of the local Hopf bifurcationsand the stability of the bifurcating periodic solutions at the first bifurcation value arederived.Finally, simulations are given to illustrate the results.lt is interesting to findthat the simulations imply the existence of global Hopf bifurcations, of the system.So atheoretical analysis of the existence of global Hopf bifurcations is given,using a globalHopf bifurcation theorem in [15].