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Dynamic Behaviors of a Single Species Stage Structure Model with Michaelis–Menten-TypeJuvenile Population Harvesting

Author

Listed:
  • Xiangqin Yu

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

  • Zhenliang Zhu

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

  • Fengde Chen

    (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China)

Abstract

A single species stage structure model with Michaelis–Menten-type juvenile population harvesting is proposed and investigated. The existence and local stability of the model equilibria are studied. It shows that for the model, two cases of bistability may exist. Some conditions for the global asymptotic stability of the boundary equilibrium are derived by constructing some suitable Lyapunov functions. After that, based on the Bendixson–Dulac discriminant, we obtain the sufficient conditions for the global asymptotic stability of the internal equilibrium. Our study shows that nonlinear harvesting can make the dynamics of the system more complex than linear harvesting; for example, the system may admit the bistable stability property. Numeric simulations support our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1281-:d:393949
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    References listed on IDEAS

    as
    1. Xiangdong Xie & Fengde Chen & Yalong Xue, 2014. "Note on the Stability Property of a Cooperative System Incorporating Harvesting," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-5, April.
    2. 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.
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