Hopf Bifurcation Analysis With Time Delay Of The Incubator Model

In this paper we study the single-species chemostat model with time dilay.Based on [8],we analyze the Hopf bifurcation of the system which take the diluton as a parameter, and we obtain that under the conditon of the existence of positive equilibrium and if the dilution is too big or too small, the system will appear Hopf bifurcation. Furthermore,we obtain the calculating formulas abont the direction of Hopf bifurcation,the stability of bifurcating periodic solution by applying the center manifold theorem and the normal form theory. At last ,we simulate the result we have obtained with Mathematica and Matlab .