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Dynamic of a delayed predator–prey model with birth pulse and impulsive harvesting in a polluted environment

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  • Wang, Xiaohong
  • Jia, Jianwen

Abstract

In this paper, we propose a delayed predator–prey model with birth pulse and impulsive harvesting in a polluted environment. Existence conditions of the predator-extinction periodic solution are derived by developing the discrete dynamical system, which is determined by the stroboscopic map. Further, we discuss the global attractivity of predator-extinction periodic solution and permanence of the system, and obtain the threshold conditions. The results provide a dependable theoretical strategies to protect population from extinction in a polluted environment. Finally, the numerical simulations are presented for verifying the theoretical conclusions.

Suggested Citation

  • Wang, Xiaohong & Jia, Jianwen, 2015. "Dynamic of a delayed predator–prey model with birth pulse and impulsive harvesting in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 1-15.
    • Handle: RePEc:eee:phsmap:v:422:y:2015:i:c:p:1-15
    DOI: 10.1016/j.physa.2014.12.003
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    References listed on IDEAS

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    1. De Rosis, Alessandro, 2014. "Hydrodynamic effects on a predator approaching a group of preys," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 329-339.
    2. 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.
    3. Zhao, Zhong & Wu, Xianbin, 2014. "Nonlinear analysis of a delayed stage-structured predator–prey model with impulsive effect and environment pollution," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1262-1268.
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    Cited by:

    1. Zhang, Yan & Chen, Shihua & Gao, Shujing & Wei, Xiang, 2017. "Stochastic periodic solution for a perturbed non-autonomous predator–prey model with generalized nonlinear harvesting and impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 347-366.

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