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Volume 8, Number 2, 2018, Pages 573-597                                                                DOI:10.11948/2018.573
Stability and Hopf bifurcation of a modified delay predator-prey model with stage structure
Jing Li,Shaotao Zhu,Ruilan Tian,Wei Zhang and Xin Li
Keywords:Delayed differential equation, hypernormal form, equilibrium point, stability, Hopf bifurcation.
      In this paper, a modified delay predator-prey model with stage structure is established, which involves the economic factor and internal competition of all the prey and predator populations. By the methods of normal form and characteristic equation, we obtain the stability of the positive equilibrium point and the sufficient condition of the existence of Hopf bifurcation. We analyze the influence of the time delay on the equation and show the occurrence of Hopf bifurcation periodic solution. The simulation gives a visual understanding for the existence and direction of Hopf bifurcation of the model.
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