With Time Delay And Holling Functional Response Of Predator - Prey System Stability And Hopf Bifurcation

This paper studies stability and bifurcation of positive equilibrium in a Predator- prey model with a delay and Holling type functional response function, where T is parameter.We find that for delay r , system exists stability switch ,that is,when r undergoes some values,the stability of positive eqilibrium alters,from asymptotically stable to unstable,then to asymptotically stable.These r are Hopf bifurcation values of the system. We exhibit calculating formula about direction of Hopf bifurcation and the bifurcation periodic solutions in the first bifurcated TO and so on with norm form theory and center mainfold theorem,Furthermore,we carry out numerical simulated compution with Mathematica.Finally,the charting are performed with Mat-lab.