IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v266y2015icp539-559.html
   My bibliography  Save this article

Permanence and asymptotical behavior of stochastic prey–predator system with Markovian switching

Author

Listed:
  • Ouyang, Mengqian
  • Li, Xiaoyue

Abstract

In this paper, we investigate the stochastic permanence and extinction of a stochastic ratio-dependent prey–predator model controlled by a Markov chain. In the permanent case we estimate the superior limit and the inferior limit of the average in time of the sample path of the solution. The boundaries are related to the stationary probability distribution of the Markov chain and the parameters of the subsystems. Finally, we illustrate our main results by two examples and some numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:539-559
    DOI: 10.1016/j.amc.2015.05.083
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315007079
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.05.083?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. Yuan, Chenggui & Mao, Xuerong, 2004. "Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 223-235.
    2. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
    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. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    2. 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.
    3. Wang, Sheng & Wang, Linshan & Wei, Tengda, 2018. "Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 294-311.
    4. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2020. "Permanence of hybrid competitive Lotka–Volterra system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Mondal, Bapin & Ghosh, Uttam & Rahman, Md Sadikur & Saha, Pritam & Sarkar, Susmita, 2022. "Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 111-135.
    6. Guirong Liu & Rong Liu, 2019. "Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response," Complexity, Hindawi, vol. 2019, pages 1-19, November.

    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. Jiang, Daqing & Zuo, Wenjie & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Stationary distribution and periodic solutions for stochastic Holling–Leslie predator–prey systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 16-28.
    2. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    3. Xie, Falan & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2017. "Periodic solution of a stochastic HBV infection model with logistic hepatocyte growth," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 630-641.
    4. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    5. Liu, Yuting & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2016. "Stochastic extinction and persistence of a parasite–host epidemiological model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 586-602.
    6. Liu, Meng & Bai, Chuanzhi, 2015. "A remark on a stochastic logistic model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 521-526.
    7. Gao, Xiangyu & Liu, Yi & Wang, Yanxia & Yang, Hongfu & Yang, Maosong, 2021. "Tamed-Euler method for nonlinear switching diffusion systems with locally Hölder diffusion coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    9. Liu, Yan & Yu, Pinrui & Chu, Dianhui & Su, Huan, 2019. "Stationary distribution of stochastic Markov jump coupled systems based on graph theory," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 188-195.
    10. Shi, Zhenfeng & Jiang, Daqing, 2022. "Dynamical behaviors of a stochastic HTLV-I infection model with general infection form and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    11. Zhao, Jingjun & Yi, Yulian & Xu, Yang, 2021. "Strong convergence of explicit schemes for highly nonlinear stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    12. Fan, Zhencheng, 2017. "Convergence of numerical solutions to stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 176-187.
    13. Debasis Mukherjee, 2022. "Stochastic Analysis of an Eco-Epidemic Model with Biological Control," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2539-2555, December.
    14. 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.
    15. Zhang, Qiumei & Jiang, Daqing, 2021. "Dynamics of stochastic predator-prey systems with continuous time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    16. Cañada, Héctor & Romera, Rosario, 2012. "Controlled diffusion processes with Markovian switchings for modeling dynamical engineering systems," European Journal of Operational Research, Elsevier, vol. 221(3), pages 614-624.
    17. Xinghu Jin & Tian Shen & Zhonggen Su, 2023. "Using Stein’s Method to Analyze Euler–Maruyama Approximations of Regime-Switching Jump Diffusion Processes," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1797-1828, September.
    18. Yang, Bo, 2018. "A stochastic Feline immunodeficiency virus model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 448-458.
    19. Yang Li & Taitao Feng & Yaolei Wang & Yifei Xin, 2021. "A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models," Mathematics, MDPI, vol. 9(6), pages 1-15, March.
    20. Zhang, Zhenzhong & Zhou, Tiandao & Jin, Xinghu & Tong, Jinying, 2020. "Convergence of the Euler–Maruyama method for CIR model with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 192-210.

    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:eee:apmaco:v:266:y:2015:i:c:p:539-559. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.