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The Asymptotic Behavior of a Stochastic Predator‐Prey System with Holling II Functional Response

Author

Listed:
  • Zhenwen Liu
  • Ningzhong Shi
  • Daqing Jiang
  • Chunyan Ji

Abstract

We discuss a stochastic predator‐prey system with Holling II functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we deduce the conditions that there is a stationary distribution of the system, which implies that the system is permanent. At last, we give the conditions for the system that is going to be extinct.

Suggested Citation

  • Zhenwen Liu & Ningzhong Shi & Daqing Jiang & Chunyan Ji, 2012. "The Asymptotic Behavior of a Stochastic Predator‐Prey System with Holling II Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:801812
    DOI: 10.1155/2012/801812
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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 & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    3. 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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    Cited by:

    1. Shuangyun Xing & Qingling Zhang & Yi Zhang, 2013. "Finite‐Time Stability Analysis and Control for a Class of Stochastic Singular Biological Economic Systems Based on T‐S Fuzzy Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yingjia Guo, 2014. "The Stability of Solutions for a Fractional Predator‐Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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