HOPF BIFURCATION ANALYSIS FOR A DELAYED PREDATOR-PREY SYSTEM WITH A PREY REFUGE AND SELECTIVE HARVESTING

Miao Peng; Zhengdi Zhang; Xuedi Wang; Xiuyu Liu

doi:10.11948/2018.982

2018 Volume 8 Issue 3

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Miao Peng, Zhengdi Zhang, Xuedi Wang, Xiuyu Liu. HOPF BIFURCATION ANALYSIS FOR A DELAYED PREDATOR-PREY SYSTEM WITH A PREY REFUGE AND SELECTIVE HARVESTING[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 982-997. doi: 10.11948/2018.982

Citation:

Miao Peng, Zhengdi Zhang, Xuedi Wang, Xiuyu Liu. HOPF BIFURCATION ANALYSIS FOR A DELAYED PREDATOR-PREY SYSTEM WITH A PREY REFUGE AND SELECTIVE HARVESTING[J]. Journal of Applied Analysis & Computation, 2018, 8(3): 982-997. doi: 10.11948/2018.982

HOPF BIFURCATION ANALYSIS FOR A DELAYED PREDATOR-PREY SYSTEM WITH A PREY REFUGE AND SELECTIVE HARVESTING

Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, China

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Abstract

Abstract

In this paper, a delayed predator-prey system with Holling type Ⅲ functional response incorporating a prey refuge and selective harvesting is considered. By analyzing the corresponding characteristic equations, the conditions for the local stability and existence of Hopf bifurcation for the system are obtained, respectively. By utilizing normal form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations supporting the theoretical analysis are given.
- Predator-prey system /
- prey refuge /
- selective harvesting /
- local stability /
- Hopf bifurcation
MSC: 34C23;34D20;34K18;34K20

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References

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