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Stochastic Delay Logistic Model under Regime Switching

Author

Listed:
  • Zheng Wu
  • Hao Huang
  • Lianglong Wang

Abstract

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall′s inequality, and Young′s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue of V‐function technique, M‐matrix method, and Chebyshev′s inequality. Finally, an example is given to illustrate the main results.

Suggested Citation

  • Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Stochastic Delay Logistic Model under Regime Switching," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:241702
    DOI: 10.1155/2012/241702
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    References listed on IDEAS

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    1. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Zhanhua Yu, 2011. "Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Zhanhua Yu, 2011. "Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, August.
    4. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, May.
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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).
    3. Ouyang, Mengqian & Li, Xiaoyue, 2015. "Permanence and asymptotical behavior of stochastic prey–predator system with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 539-559.
    4. Meng Liu & Ke Wang, 2013. "Stochastic Differential Equations with Multi‐Markovian Switching," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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