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Dynamical Behavior of a Stochastic Ratio‐Dependent Predator‐Prey System

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  • Zheng Wu
  • Hao Huang
  • Lianglong Wang

Abstract

This paper is concerned with a stochastic ratio‐dependent predator‐prey model with varible coefficients. By the comparison theorem of stochastic equations and the Itô formula, the global existence of a unique positive solution of the ratio‐dependent model is obtained. Besides, some results are established such as the stochastically ultimate boundedness and stochastic permanence for this model.

Suggested Citation

  • Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Dynamical Behavior of a Stochastic Ratio‐Dependent Predator‐Prey System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:857134
    DOI: 10.1155/2012/857134
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    References listed on IDEAS

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    1. Ileana Miranda Cabrera & Heyker Lellanis Baños Díaz & María de los Ángeles Martínez, 2010. "Dynamical System and Nonlinear Regression for Estimate Host‐Parasitoid Relationship," Journal of Applied Mathematics, John Wiley & Sons, vol. 2010(1).
    2. Scott A. Hadley & Lawrence K. Forbes, 2009. "Dynamical Systems Analysis of a Five‐Dimensional Trophic Food Web Model in the Southern Oceans," Journal of Applied Mathematics, John Wiley & Sons, vol. 2009(1).
    3. Scott A. Hadley & Lawrence K. Forbes, 2009. "Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans," Journal of Applied Mathematics, Hindawi, vol. 2009, pages 1-17, February.
    4. Ileana Miranda Cabrera & Heyker Lellanis Baños Díaz & María de los Ángeles Martínez, 2010. "Dynamical System and Nonlinear Regression for Estimate Host-Parasitoid Relationship," Journal of Applied Mathematics, Hindawi, vol. 2010, pages 1-10, November.
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    Cited by:

    1. Zheng Wu & Hao Huang & Lianglong Wang, 2013. "Stochastic Delay Population Dynamics under Regime Switching: Permanence and Asymptotic Estimation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Zheng Wu & Hao Huang & Lianglong Wang, 2013. "Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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