STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE

Jing Li; Shaotao Zhu; Ruilan Tian; Wei Zhang; Xin Li

doi:10.11948/2018.573

2018 Volume 8 Issue 2

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Jing Li, Shaotao Zhu, Ruilan Tian, Wei Zhang, Xin Li. STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 573-597. doi: 10.11948/2018.573

Citation:

Jing Li, Shaotao Zhu, Ruilan Tian, Wei Zhang, Xin Li. STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 573-597. doi: 10.11948/2018.573

STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE

1 College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China;
2 Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China;
3 College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, 100124, China

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Abstract

Abstract

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.
- Delayed differential equation /
- hypernormal form /
- equilibrium point /
- stability /
- Hopf bifurcation
MSC: 34C37;35Q51

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References

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