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Persistence and Nonpersistence of a Nonautonomous Stochastic Mutualism System

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  • Peiyan Xia
  • Xiaokun Zheng
  • Daqing Jiang

Abstract

In this paper, a two-species nonautonomous stochastic mutualism system is investigated. The intrinsic growth rates of the two species at time are estimated by respectively. Viewing the different intensities of the noises , as two parameters at time , we conclude that there exists a global positive solution and the th moment of the solution is bounded. We also show that the system is permanent, including stochastic permanence, persistence in mean, and asymptotic boundedness in time average. Besides, we show that the large white noise will make the system nonpersistent. Finally, we establish sufficient criteria for the global attractivity of the system.

Suggested Citation

  • Peiyan Xia & Xiaokun Zheng & Daqing Jiang, 2013. "Persistence and Nonpersistence of a Nonautonomous Stochastic Mutualism System," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, February.
    • Handle: RePEc:hin:jnlaaa:256249
    DOI: 10.1155/2013/256249
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    Cited by:

    1. El Fatini, M. & Taki, R. & Tridane, A., 2019. "Threshold behaviour of a stochastic epidemic model with two-dimensional noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 776-786.
    2. Settati, A. & Lahrouz, A. & Assadouq, A. & El Fatini, M. & El Jarroudi, M. & Wang, K., 2020. "The impact of nonlinear relapse and reinfection to derive a stochastic threshold for SIRI epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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