With Control Holling Type Iii Predator - Prey System Of Hopf Bifurcation And Periodic Solutions

In this paper,a controlling Predator-prey system model of HollingⅢtype is considered.Whenτis equal to zero(no control item),the conditions of existence and local stability and bifurcation for the steady-states are obtained and the periodic solution of the Hopf type are considered.Whenτis not equal to zero(have control item),the conditions of existence of Hopf bifurcations and Hopf bifurcations coccur when the delayτpasses through a sequence of critical values,whereτis regarded as parameter.We have computed formula which determine the stability direction and other properties of bifurcating periodic solutions are derived by use Hassard method.We have given numerical simulation to verify some of the key results we have obtained.This paper is organized as follows:In Introduction,some fundamental definitions theories are introduced;In Chapter 1,some preliminary knowledge are presented;In Chapter 2 and Chapter 3,some analysis of the model is doing; In Chapter 4,some numerical simulations are performed to illustrate the analytical results found.In Chapter 5,our paper end with a brief conclusion.