IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n426702.html

Dynamical Behavior of a Stochastic Food‐Chain System with Beddington‐DeAngelis Functional Response

Author

Listed:
  • Yanming Ge
  • Zigen Song

Abstract

We investigate a stochastic Food‐Chain System dx(t) = [r1(t) − a11(t)x − (a12(t)y/(1 + β1(t)x + γ1(t)y))]xdt + σ1(t)xdB1(t), dy(t) = [r2(t) − a21(t)y + (a22(t)x/(1 + β1(t)x + γ1(t)y)) − (a23(t)z/(1 + β2(t)y + γ2(t)z))]ydt + σ2(t)ydB2(t), dz(t) = [−r3(t) + (a31(t)y/(1 + β2(t)y + γ2(t)z)) − a32(t)z]zdt + σ3(t)zdB3(t), where Bi(t), i = 1, 2, 3, is a standard Brownian motion. Firstly, the existence, the uniqueness, and the positivity of the solution are proved. Secondly, the stochastically ultimate boundedness of the system is investigated. Thirdly, the boundedness of moments and upper‐growth rate of the solution are obtained. Then the global attractivity of the system is discussed. Finally, the main results are illustrated by several examples.

Suggested Citation

  • Yanming Ge & Zigen Song, 2014. "Dynamical Behavior of a Stochastic Food‐Chain System with Beddington‐DeAngelis Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:426702
    DOI: 10.1155/2014/426702
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/426702
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/426702?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Verdy, Ariane, 2010. "Modulation of predator–prey interactions by the Allee effect," Ecological Modelling, Elsevier, vol. 221(8), pages 1098-1107.
    2. Gan, Qintao & Xu, Rui & Yang, Pinghua, 2009. "Bifurcation and chaos in a ratio-dependent predator–prey system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1883-1895.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.
    2. Gui-Quan Sun & Li Li & Zhen Jin & Zi-Ke Zhang & Tao Zhou, 2013. "Pattern Dynamics in a Spatial Predator‐Prey System with Allee Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    4. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
    5. Hu, Guang-Ping & Li, Wan-Tong & Yan, Xiang-Ping, 2009. "Hopf bifurcations in a predator–prey system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1273-1285.
    6. Li, Danyang & Liu, Hua & Zhang, Haotian & Wei, Yumei, 2023. "Influence of multiple delays mechanisms on predator–prey model with Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Wang, Zhen & Xie, Yingkang & Lu, Junwei & Li, Yuxia, 2019. "Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 360-369.
    8. Boli Xie & Zhijun Wang & Yakui Xue & Zhenmin Zhang, 2015. "The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, October.
    9. Barman, Dipesh & Kumar Upadhyay, Ranjit, 2026. "Impact of carryover and fear-induced delays on population dynamics: A cross-model stability and bifurcation investigation," Applied Mathematics and Computation, Elsevier, vol. 516(C).
    10. Iskin da S. Costa, Michel & dos Anjos, Lucas, 2018. "Multiple hydra effect in a predator–prey model with Allee effect and mutual interference in the predator," Ecological Modelling, Elsevier, vol. 373(C), pages 22-24.
    11. Pal, Pallav Jyoti & Mandal, Gourav & Guin, Lakshmi Narayan & Saha, Tapan, 2024. "Allee effect and hunting-induced bifurcation inquisition and pattern formation in a modified Leslie–Gower interacting species system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:426702. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.