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An Impulsive Three‐Species Model with Square Root Functional Response and Mutual Interference of Predator

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Listed:
  • Zhen Wang
  • Yuanfu Shao
  • Xianjia Fang
  • Xiangmin Ma

Abstract

An impulsive two‐prey and one‐predator model with square root functional responses, mutual interference, and integrated pest management is constructed. By using techniques of impulsive perturbations, comparison theorem, and Floquet theory, the existence and global asymptotic stability of prey‐eradication periodic solution are investigated. We use some methods and sufficient conditions to prove the permanence of the system which involve multiple Lyapunov functions and differential comparison theorem. Numerical simulations are given to portray the complex behaviors of this system. Finally, we analyze the biological meanings of these results and give some suggestions for feasible control strategies.

Suggested Citation

  • Zhen Wang & Yuanfu Shao & Xianjia Fang & Xiangmin Ma, 2016. "An Impulsive Three‐Species Model with Square Root Functional Response and Mutual Interference of Predator," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:3897234
    DOI: 10.1155/2016/3897234
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    References listed on IDEAS

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    1. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 980-990.
    2. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type II predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 367-376.
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