| In this paper, by using the method of characteristic root and analytic, the stability of the positive equilibrium for two classes of delayed Watt-type predator-prey models are analyzed. Then, by applying the theorem of Hopf bifurcation and the existence of Hopf bifurcations is obtained. Then, by applying the center manifold argument and normal form theory, the character of Hopf bifurcation is studied.The introduction is shown in Chapter one. The background, research value and the current situation of Watt-type predator-prey models are discussed. Then, the main content of this paper are presented.A Watt-type predator-prey models with two same delayed is discussed in Chapter two, by using the method of characteristic root and analytic to analysis the stability of the positive equilibrium and regarding the delayτas the bifurcation parameter, the existence of Hopf bifurcations is obtained. Then, by using the center manifold argument and normal form theory, the formula to calculate the period of bifurcation periodic solutions and decide the stability of bifurcation periodic solutions, the bifurcation direction. The existing relevant conclusions of such system have been promoted and improved in this chapter.A Watt-type predator-prey system with two different delays is investigated in Chapter three. By using the new way and selecting the delaysτ1,τ2 as bifurcation parameter in proper order, the stability of zero solution is discussed,and the existence of Hopf bifurcations is obtained. Its biological meaning showed that the two groups will coexist eventually in the form of periodic oscillations. A Watt-type predator-prey system with two different delays is studied firstly in this chapter, It is found that the stability of zero solution is impacted by the two delays in the sme time. The existing literature related to conclusions have been improved and supplemented by our results in this chapter. Finally, the summary and the need for the further research are shown. |
PDF Full Text Request