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Dynamics of an impulsive predator–prey logistic population model with state-dependent

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  • Xiao, Qizhen
  • Dai, Binxiang

Abstract

In this paper, the dynamics for a class of state-dependent impulsive predator–prey models with the logistic growth for the predator and prey species are analyzed. By a direct calculation, the existence of a semi-trivial periodic solution is obtained. Based on the geometrical analysis and biological background, the strict threshold value conditions for the existence of positive periodic solutions are depicted. The stabilities of the semi-trivial periodic solution and positive order-1 periodic solutions are proved due to the analogue of Poincaré criterion. Numerical results are carried out to illustrate the feasibility of our main results.

Suggested Citation

  • Xiao, Qizhen & Dai, Binxiang, 2015. "Dynamics of an impulsive predator–prey logistic population model with state-dependent," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 220-230.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:220-230
    DOI: 10.1016/j.amc.2015.02.061
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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. Guo, Hongjian & Song, Xinyu, 2008. "An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1320-1331.
    3. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
    4. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2392-2404.
    5. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2008. "Chaotic behavior of a Watt-type predator–prey system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 706-718.
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    Cited by:

    1. Jiang, Fangfang & Sun, Jitao, 2016. "On the existence of discontinuous periodic solutions for a class of Liénard systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 259-265.
    2. Ihsan Ullah Khan & Sanyi Tang & Biao Tang, 2019. "The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate," Complexity, Hindawi, vol. 2019, pages 1-15, June.

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