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The dynamics of an impulsive predator–prey model with communicable disease in the prey species only

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  • Xie, Youxiang
  • Wang, Linjun
  • Deng, Qicheng
  • Wu, Zhengjia

Abstract

In this paper, we propose an impulsive predator–prey model with communicable disease in the prey species only and investigate its interesting biological dynamics. By the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we have deduced the sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the proposed model. We also give the existences of the “infection-free” periodic solution and the “predator-free” solution. Finally, numerical results validate the effectiveness of theoretical analysis for the proposed model in this paper.

Suggested Citation

  • Xie, Youxiang & Wang, Linjun & Deng, Qicheng & Wu, Zhengjia, 2017. "The dynamics of an impulsive predator–prey model with communicable disease in the prey species only," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 320-335.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:320-335
    DOI: 10.1016/j.amc.2016.07.042
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    References listed on IDEAS

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    4. Benjamin L. Phillips & Gregory P. Brown & Jonathan K. Webb & Richard Shine, 2006. "Invasion and the evolution of speed in toads," Nature, Nature, vol. 439(7078), pages 803-803, February.
    5. Liu, Zhijun & Chen, Lansun, 2007. "Periodic solution of a two-species competitive system with toxicant and birth pulse," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1703-1712.
    6. Lin Wang & Xiang Li & Yi-Qing Zhang & Yan Zhang & Kan Zhang, 2011. "Evolution of Scaling Emergence in Large-Scale Spatial Epidemic Spreading," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-11, July.
    7. Hui, Jing & Chen, Lansun, 2006. "Dynamic complexities in a periodically pulsed ratio-dependent predator–prey ecosystem modeled on a chemostat," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 407-416.
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    Cited by:

    1. Li, Hong-Li & Zhang, Long & Teng, Zhidong & Jiang, Yao-Lin & Muhammadhaji, Ahmadjan, 2018. "Global stability of an SI epidemic model with feedback controls in a patchy environment," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 372-384.

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