IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i4d10.1007_s11009-020-09824-8.html
   My bibliography  Save this article

Analysis of a Stochastic Competitive Model with Saturation Effect and Distributed Delay

Author

Listed:
  • Wenxu Ning

    (Hubei Minzu University)

  • Zhijun Liu

    (Hubei Minzu University)

  • Lianwen Wang

    (Hubei Minzu University)

  • Ronghua Tan

    (Hubei Minzu University)

Abstract

This work is concerned with a novel stochastic competitive model with saturation effect and distributed delay, in which two coupling noise sources are incorporated and the interspecific competition delayed terms show saturation effect. A good understanding of exponential extinction, extinction, persistence in the mean and permanence in time average of two species are gained. Also, with the help of Lyapunov function and the global attraction of positive solution, we derive the existence and uniqueness of stationary distribution. Our main results reveal that the coupling noise sources can significantly change the survival results of two species and affect the existence of a unique stationary distribution.

Suggested Citation

  • Wenxu Ning & Zhijun Liu & Lianwen Wang & Ronghua Tan, 2021. "Analysis of a Stochastic Competitive Model with Saturation Effect and Distributed Delay," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1435-1459, December.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09824-8
    DOI: 10.1007/s11009-020-09824-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09824-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-020-09824-8?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    2. Sun, Xinguo & Zuo, Wenjie & Jiang, Daqing & Hayat, Tasawar, 2018. "Unique stationary distribution and ergodicity of a stochastic Logistic model with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 864-881.
    3. Zuo, Wenjie & Jiang, Daqing & Sun, Xinguo & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Long-time behaviors of a stochastic cooperative Lotka–Volterra system with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 542-559.
    4. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    5. Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Han, Bingtao & Jiang, Daqing, 2022. "Stationary distribution, extinction and density function of a stochastic prey-predator system with general anti-predator behavior and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    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. Lu, Chun, 2021. "Dynamics of a stochastic Markovian switching predator–prey model with infinite memory and general Lévy jumps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 316-332.
    2. Cao, Nan & Fu, Xianlong, 2023. "Stationary distribution and extinction of a Lotka–Volterra model with distribute delay and nonlinear stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution and extinction of a stochastic ratio-dependent predator–prey system with stage structure for the predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Han, Bingtao & Jiang, Daqing, 2022. "Stationary distribution, extinction and density function of a stochastic prey-predator system with general anti-predator behavior and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    6. Li, Qiuyue & Cong, Fuzhong & Liu, Tianbao & Zhou, Yaoming, 2020. "Stationary distribution of a stochastic HIV model with two infective stages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    7. Zhang, Xiaofeng & Yuan, Rong, 2022. "Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and weak kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 56-70.
    8. Eva Kaslik & Mihaela Neamţu & Loredana Flavia Vesa, 2021. "Global Stability Analysis of a Five-Dimensional Unemployment Model with Distributed Delay," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    9. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 199-210.
    10. Liu, Meng & Bai, Chuanzhi, 2020. "Optimal harvesting of a stochastic mutualism model with regime-switching," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    11. Liu, Yanwei & Zhang, Tonghua & Liu, Xia, 2020. "Investigating the interactions between Allee effect and harvesting behaviour of a single species model: An evolutionary dynamics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    12. Kim, Sangkwon & Park, Jintae & Lee, Chaeyoung & Jeong, Darae & Choi, Yongho & Kwak, Soobin & Kim, Junseok, 2020. "Periodic travelling wave solutions for a reaction-diffusion system on landscape fitted domains," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Pimentel, Carlos Eduardo Hirth & Rodriguez, Pablo M. & Valencia, Leon A., 2020. "A note on a stage-specific predator–prey stochastic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    14. Xiaomei Feng & Yuan Miao & Shulin Sun & Lei Wang, 2022. "Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    15. Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    16. Wang, Fatao & Yang, Ruizhi & Zhang, Xin, 2024. "Turing patterns in a predator–prey model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 170-191.
    17. Yuke Zhang & Xinzhu Meng, 2022. "Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    18. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    19. Zhan, Jinxiang & Wei, Yongchang, 2024. "Dynamical behavior of a stochastic non-autonomous distributed delay heroin epidemic model with regime-switching," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    20. Jiang, Yan & Zhai, Junyong, 2019. "Observer-based stabilization of sector-bounded nonlinear stochastic systems in the presence of intermittent measurements," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 740-752.

    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:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09824-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.