IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v256y2015icp52-67.html

Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments

Author

Listed:
  • Liu, Qun
  • Chen, Qingmei

Abstract

In this paper, two stochastic delay Lotka–Volterra systems (i.e., competition system and predator–prey system) with impulsive toxicant input and Lévy noise in polluted environments are proposed and investigated. Under some simple assumptions, sufficient and necessary criteria for stability in time average and extinction of each population are established. The thresholds between stability in time average and extinction of each model are obtained. Some recent results are improved and extended greatly.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:52-67
    DOI: 10.1016/j.amc.2015.01.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315000235
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.01.009?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
    2. 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.
    3. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.
    4. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    5. Jiao, Jianjun & Ye, Kaili & Chen, Lansun, 2011. "Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 17-27.
    6. Wan, Li & Zhou, Qinghua, 2009. "Stochastic Lotka-Volterra model with infinite delay," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 698-706, March.
    7. 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. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    2. Liu, Meng & Bai, Chuanzhi & Deng, Meiling & Du, Bo, 2016. "Analysis of stochastic two-prey one-predator model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 176-188.

    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. Meng Liu, 2013. "Analysis of Stochastic Delay Predator‐Prey System with Impulsive Toxicant Input in Polluted Environments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    3. 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.
    4. Qin, Wenjie & Zhao, Yi & Yang, Jin, 2025. "Modeling the effects of obesity on a tumor-immune model with combined therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 276-295.
    5. Wenbin Liu, 2013. "A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. 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).
    7. Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
    8. 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.
    9. 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).
    10. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
    11. Zuwen Wang & Shaojian Cai & Guangmin Chen & Kuicheng Zheng & Fengying Wei & Zhen Jin & Xuerong Mao & Jianfeng Xie, 2024. "Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations," Mathematics, MDPI, vol. 12(16), pages 1-26, August.
    12. Yang, Jiangtao, 2020. "Threshold behavior in a stochastic predator–prey model with general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    13. Liyan Wang & Huilin Huang & Ancha Xu & Weiming Wang, 2013. "Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    14. Yuxiao Zhao & Linshan Wang, 2022. "Practical Exponential Stability of Impulsive Stochastic Food Chain System with Time-Varying Delays," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    15. Bing Liu & Ling Xu & Baolin Kang, 2013. "Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    16. Yongli Cai & Xixi Wang & Weiming Wang & Min Zhao, 2013. "Stochastic Dynamics of an SIRS Epidemic Model with Ratio‐Dependent Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:apmaco:v:256:y:2015:i:c:p:52-67. 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.