IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v92y2013icp53-75.html
   My bibliography  Save this article

Dynamics and simulations of a logistic model with impulsive perturbations in a random environment

Author

Listed:
  • Liu, Meng
  • Wang, Ke

Abstract

A stochastic logistic model with Markovian switching and impulsive perturbations is proposed and investigated. Firstly, we show that this model has a global and positive solution. Then we establish the sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence of the solution. The critical value between weak persistence and extinction is obtained. Afterwards we study some asymptotic properties of this model. The lower- and the upper-growth rates of the positive solution are investigated. The superior limit of the average in time of the sample path of the solution is also estimated. Finally, some simulation figures are introduced to illustrate the main results.

Suggested Citation

  • Liu, Meng & Wang, Ke, 2013. "Dynamics and simulations of a logistic model with impulsive perturbations in a random environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 53-75.
    • Handle: RePEc:eee:matcom:v:92:y:2013:i:c:p:53-75
    DOI: 10.1016/j.matcom.2013.04.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475413000773
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2013.04.011?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. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    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. Sun, Li & Zhu, Haitao & Ding, Yanhui, 2020. "Impulsive control for persistence and periodicity of logistic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 294-305.
    2. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).
    3. Guo, Xiaoxia & Luo, Jiaowan, 2018. "Stationary distribution and extinction of SIR model with nonlinear incident rate under Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 471-481.

    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. Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.
    2. Huang, Zaitang & Cao, Junfei, 2018. "Ergodicity and bifurcations for stochastic logistic equation with non-Gaussian Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 1-10.
    3. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    4. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    5. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    6. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    7. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    8. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    9. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    10. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    11. El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    12. 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).
    13. Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.
    14. 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).
    15. Kostić, Vladimir R. & Cvetković, Ljiljana & Cvetković, Dragana Lj., 2016. "Improved stability indicators for empirical food webs," Ecological Modelling, Elsevier, vol. 320(C), pages 1-8.
    16. Liu, Qun & Jiang, Daqing, 2020. "Dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    17. Quentin Clairon & Adeline Samson, 2020. "Optimal control for estimation in partially observed elliptic and hypoelliptic linear stochastic differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 105-127, April.
    18. Guo, Qing & Wang, Yi & Dai, Chuanjun & Wang, Lijun & Liu, He & Li, Jianbing & Tiwari, Pankaj Kumar & Zhao, Min, 2023. "Dynamics of a stochastic nutrient–plankton model with regime switching," Ecological Modelling, Elsevier, vol. 477(C).
    19. Lu, Chun & Ding, Xiaohua, 2019. "Periodic solutions and stationary distribution for a stochastic predator-prey system with impulsive perturbations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 313-322.
    20. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li & Gao, Jinyao, 2020. "Nontrivial periodic solution of a stochastic seasonal rabies epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

    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:matcom:v:92:y:2013:i:c:p:53-75. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.