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An impulsive two-stage predator–prey model with stage-structure and square root functional responses

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Listed:
  • Ma, Xiangmin
  • Shao, Yuanfu
  • Wang, Zhen
  • Luo, Mengzhuo
  • Fang, Xianjia
  • Ju, Zhixiang

Abstract

Taking into account stage-structure for predator and periodic pulse at different fixed moment, a delayed predator–prey system with square root functional response is investigated in this paper. Sufficient conditions for the global attractivity of the mature predator-extinction periodic solution are obtained. Further, by using theories of impulsive differential equation and delay differential equation, we investigate the permanence of this system. Finally, examples and numerical simulations are given to show that time delays and pulses play an important role in the dynamics which makes the system be more complex.

Suggested Citation

  • Ma, Xiangmin & Shao, Yuanfu & Wang, Zhen & Luo, Mengzhuo & Fang, Xianjia & Ju, Zhixiang, 2016. "An impulsive two-stage predator–prey model with stage-structure and square root functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 91-107.
    • Handle: RePEc:eee:matcom:v:119:y:2016:i:c:p:91-107
    DOI: 10.1016/j.matcom.2015.08.009
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Singh, Brahampal, 2007. "The dynamics of a food web consisting of two preys and a harvesting predator," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1346-1356.
    2. Jiao, Jianjun & Meng, Xinzhu & Chen, Lansun, 2009. "Harvesting policy for a delayed stage-structured Holling II predator–prey model with impulsive stocking prey," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 103-112.
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    Cited by:

    1. Wang, Zhen & Shao, Yuanfu & Fang, Xianjia & Ma, Xiangmin, 2017. "The dynamic behaviors of one-predator two-prey system with mutual interference and impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 68-85.
    2. Maiti, Atasi Patra & Dubey, B. & Chakraborty, A., 2019. "Global analysis of a delayed stage structure prey–predator model with Crowley–Martin type functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 58-84.
    3. dos Anjos, Lucas & Weber, Igor Daniel & Godoy, Wesley Augusto Conde, 2023. "Modelling the biocontrol of Spodoptera frugiperda: A mechanistic approach considering Bt crops and oviposition behaviour," Ecological Modelling, Elsevier, vol. 484(C).
    4. Yu, Tianhu & Cao, Dengqing & Yang, Yang & Liu, Shengqiang & Huang, Wenhu, 2016. "Robust synchronization of impulsively coupled complex dynamical network with delayed nonidentical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 92-101.
    5. Fu, Shuaiming & Luo, Jianfeng & Zhao, Yi, 2022. "Stability and bifurcations analysis in an ecoepidemic system with prey group defense and two infectious routes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 665-690.
    6. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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