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Dynamical Analysis of a Stochastic Predator‐Prey Model with an Allee Effect

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  • Feng Rao

Abstract

We present and analyze a modified Holling type‐II predator‐prey model that includes some important factors such as Allee effect, density‐dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.

Suggested Citation

  • Feng Rao, 2013. "Dynamical Analysis of a Stochastic Predator‐Prey Model with an Allee Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:340980
    DOI: 10.1155/2013/340980
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    References listed on IDEAS

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    1. Xixi Wang & Huilin Huang & Yongli Cai & Weiming Wang, 2012. "The Complex Dynamics of a Stochastic Predator-Prey Model," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, September.
    2. Xixi Wang & Huilin Huang & Yongli Cai & Weiming Wang, 2012. "The Complex Dynamics of a Stochastic Predator‐Prey Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Complex dynamics of a Holling type II prey–predator system with state feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 448-461.
    4. Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.
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    Cited by:

    1. Jevgeņijs Carkovs & Jolanta Goldšteine & Kārlis Šadurskis, 2018. "The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    2. Feng Rao & Shunjun Jiang & Yanqiu Li & Hao Liu, 2013. "Stochastic Analysis of a Hassell‐Varley Type Predation Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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