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Periodic solutions and stationary distribution of mutualism models in random environments

Author

Listed:
  • Zhang, Xinhong
  • Jiang, Daqing
  • Alsaedi, Ahmed
  • Hayat, Tasawar

Abstract

This paper is concerned with mutualism models in random environments. For the periodic mutualism model disturbed by white noise, using Has’minskii theory of periodic solution, we show that this model admits a nontrivial positive periodic solution. Then sufficient conditions for the existence and global attractivity of the boundary periodic solutions are established. For the mutualism model disturbed by both white noise and telephone noise, sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the solution are established. Finally, examples are introduced to illustrate the results developed.

Suggested Citation

  • Zhang, Xinhong & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2016. "Periodic solutions and stationary distribution of mutualism models in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 270-282.
    • Handle: RePEc:eee:phsmap:v:460:y:2016:i:c:p:270-282
    DOI: 10.1016/j.physa.2016.05.015
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    References listed on IDEAS

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    1. Han, Qixing & Jiang, Daqing, 2015. "Periodic solution for stochastic non-autonomous multispecies Lotka–Volterra mutualism type ecosystem," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 204-217.
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    Cited by:

    1. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Asymptotic behavior of a food-limited Lotka–Volterra mutualism model with Markovian switching and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 94-104.
    2. Zhang, Chunmei & Shi, Lin, 2021. "Graph-theoretic method on the periodicity of coupled predator–prey systems with infinite delays on a dispersal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    3. Feng, Jiqiang & Xu, Chen, 2020. "The existence of a stationary distribution for stochastic coupled oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.
    5. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    6. Wang, Hui & Pan, Fangmei & Liu, Meng, 2019. "Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 591-606.

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