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Modelling and qualitative analysis of a predator–prey system with state-dependent impulsive effects

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  • Tian, Yuan
  • Sun, Kaibiao
  • Chen, Lansun

Abstract

In this work, according to integrated pest management principles, a class of predator–prey system with state-dependent impulsive effects is put forward. In this model, the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. The sufficient conditions for the existence and stability of the semi-trivial periodic solution and the positive order-1 periodic solution are given by the Poincaré map and the properties of the Lambert W function. In addition, to verify the feasibility of our main results, the numerical simulations are carried out.

Suggested Citation

  • Tian, Yuan & Sun, Kaibiao & Chen, Lansun, 2011. "Modelling and qualitative analysis of a predator–prey system with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 318-331.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:2:p:318-331
    DOI: 10.1016/j.matcom.2011.08.003
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    References listed on IDEAS

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    1. Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Complex dynamics of a Holling type II prey–predator system with state feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 448-461.
    2. Nie, Linfei & Teng, Zhidong & Hu, Lin & Peng, Jigen, 2009. "Existence and stability of periodic solution of a predator–prey model with state-dependent impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2122-2134.
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    Cited by:

    1. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
    2. Li, Wenjie & Huang, Lihong & Guo, Zhenyuan & Ji, Jinchen, 2020. "Global dynamic behavior of a plant disease model with ratio dependent impulsive control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 120-139.
    3. Yangyang Su & Tongqian Zhang, 2022. "Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control," Mathematics, MDPI, vol. 10(8), pages 1-23, April.
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    5. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    6. Zu, Jian, 2013. "Global qualitative analysis of a predator–prey system with Allee effect on the prey species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 33-54.

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