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Dynamic Behaviors of a Harvesting Leslie-Gower Predator-Prey Model

Author

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  • Na Zhang
  • Fengde Chen
  • Qianqian Su
  • Ting Wu

Abstract

A Leslie-Gower predator-prey model incorporating harvesting is studied. By constructing a suitable Lyapunov function, we show that the unique positive equilibrium of the system is globally stable, which means that suitable harvesting has no influence on the persistent property of the harvesting system. After that, detailed analysis about the influence of harvesting is carried out, and an interesting finding is that under some suitable restriction, harvesting has no influence on the final density of the prey species, while the density of predator species is strictly decreasing function of the harvesting efforts. For the practical significance, the economic profit is considered, sufficient conditions for the presence of bionomic equilibrium are given, and the optimal harvesting policy is obtained by using the Pontryagin's maximal principle. At last, an example is given to show that the optimal harvesting policy is realizable.

Suggested Citation

  • Na Zhang & Fengde Chen & Qianqian Su & Ting Wu, 2011. "Dynamic Behaviors of a Harvesting Leslie-Gower Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-14, April.
    • Handle: RePEc:hin:jnddns:473949
    DOI: 10.1155/2011/473949
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    Cited by:

    1. Xiangqin Yu & Zhenliang Zhu & Fengde Chen, 2020. "Dynamic Behaviors of a Single Species Stage Structure Model with Michaelis–Menten-TypeJuvenile Population Harvesting," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
    2. Qiu, Huanhuan & Guo, Shangjiang, 2019. "Steady-states of a Leslie–Gower model with diffusion and advection," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 695-709.
    3. Cortés García, Christian, 2023. "Impact of prey refuge in a discontinuous Leslie-Gower model with harvesting and alternative food for predators and linear functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 147-165.

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