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Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction

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  • Zheng Wu
  • Hao Huang
  • Lianglong Wang

Abstract

This paper is concerned with a delay Lotka‐Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Finally, an example is given to illustrate the main results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:918569
    DOI: 10.1155/2013/918569
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    References listed on IDEAS

    as
    1. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Dynamical Behavior of a Stochastic Ratio-Dependent Predator-Prey System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, May.
    2. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Stochastic Delay Logistic Model under Regime Switching," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-26, July.
    3. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Exponential Stability of Impulsive Stochastic Functional Differential Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Exponential Stability of Impulsive Stochastic Functional Differential Systems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, May.
    5. 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).
    6. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Stochastic Delay Logistic Model under Regime Switching," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    Full references (including those not matched with items on IDEAS)

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