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Existence and stability of periodic solution of a predator–prey model with state-dependent impulsive effects

Author

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  • Nie, Linfei
  • Teng, Zhidong
  • Hu, Lin
  • Peng, Jigen

Abstract

According to integrated pest management for pests, we investigate the dynamic behavior of a class predator–prey system with state-dependent impulsive effects by releasing natural enemies and spraying pesticide at different thresholds. Using the Poincaré map and the properties of the Lambert W function, we prove the sufficient conditions for the existence and stability of semi-trivial solutions and positive periodic solutions. Numerical results are carried out to illustrate the feasibility of our main results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:7:p:2122-2134
    DOI: 10.1016/j.matcom.2008.11.015
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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.
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    Cited by:

    1. 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.
    2. 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.
    3. He, Zhilong & Li, Chuandong & Li, Hongfei & Zhang, Qiangqiang, 2020. "Global exponential stability of high-order Hopfield neural networks with state-dependent impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    4. 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.

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