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Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input

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  • Yang, Xiaofeng
  • Jin, Zhen
  • Xue, Yakui

Abstract

In this paper, we have investigated a predator–prey system in a polluted environment with impulsive toxicant input at fixed moments. We have obtained two thresholds on the impulsive period by assuming the toxicant amount input is fixed to the environment at each pulse moment. If the impulsive period is greater than the big threshold, then both populations are weak average persistent. If the period lies between of the two thresholds, then the prey population will be weak average persistent while the predator population extinct. If the period is less than the small threshold, both populations tend to extinction. Finally, our theoretical results are confirmed by own numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:3:p:726-735
    DOI: 10.1016/j.chaos.2005.10.042
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    References listed on IDEAS

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    1. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    2. Zhang, Shuwen & Chen, Lansun, 2005. "Chaos in three species food chain system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 73-83.
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    4. Gakkhar, Sunita & Singh, Brahampal, 2005. "Complex dynamic behavior in a food web consisting of two preys and a predator," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 789-801.
    5. Lin, Wei, 2005. "Description of complex dynamics in a class of impulsive differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1007-1017.
    6. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
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    Citations

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    Cited by:

    1. Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
    2. Liu, Chao & Xun, Xinying & Zhang, Qingling & Li, Yuanke, 2019. "Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 99-118.
    3. Yu, Xingwang & Yuan, Sanling & Zhang, Tonghua, 2019. "Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 249-264.
    4. Yang, Jin & Tan, Yuanshun & Cheke, Robert A., 2019. "Modelling effects of a chemotherapeutic dose response on a stochastic tumour-immune model," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 1-13.
    5. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    6. Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.
    7. 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.
    8. Wang, Hui & Pan, Fangmei & Liu, Meng, 2019. "Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 591-606.

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