IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i4p1572-1577.html
   My bibliography  Save this article

Impulsive control of uncertain Lotka–Volterra predator–prey system

Author

Listed:
  • Li, Dong
  • Wang, Shilong
  • Zhang, Xiaohong
  • Yang, Dan

Abstract

In this letter, we investigate the impulsive control of Lotka–Volterra predator–prey system. The uncertainties in the system are considered. The model parameters which character the uncertainties are formulated through matrix analysis. The sufficient conditions of the asymptotic stability are established by employing the method of Lyapunov functions. Finally, the validity of the results is demonstrated by a numerical example.

Suggested Citation

  • Li, Dong & Wang, Shilong & Zhang, Xiaohong & Yang, Dan, 2009. "Impulsive control of uncertain Lotka–Volterra predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1572-1577.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1572-1577
    DOI: 10.1016/j.chaos.2008.06.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908002890
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.06.021?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. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type IV predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 980-990.
    2. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaos in periodically forced Holling type II predator–prey system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 367-376.
    3. Song, Xinyu & Li, Yongfeng, 2007. "Dynamic complexities of a Holling II two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 463-478.
    4. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2008. "Chaotic behavior of a Watt-type predator–prey system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 706-718.
    5. Liu, Bing & Teng, Zhidong & Liu, Wanbo, 2007. "Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 356-370.
    6. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Dynamic complexity of a two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 131-139.
    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. Stamov, Gani Tr. & Simeonov, Stanislav & Stamova, Ivanka M., 2018. "Uncertain impulsive Lotka–Volterra competitive systems: Robust stability of almost periodic solutions," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 178-184.

    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. Guo, Hongjian & Chen, Lansun & Song, Xinyu, 2009. "Dynamic analysis of a kind of species control model concerning impulsively releasing pathogen and infective predator," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1326-1336.
    2. Jiao, Jianjun & Meng, Xinzhu & Chen, Lansun, 2009. "Harvesting policy for a delayed stage-structured Holling II predator–prey model with impulsive stocking prey," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 103-112.
    3. Chen, Yiping & Liu, Zhijun, 2009. "Modelling and analysis of an impulsive SI model with Monod-Haldane functional response," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1698-1714.
    4. Liu, Zhijun & Tan, Ronghua, 2007. "Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 454-464.
    5. Wang, Xiaoqin & Wang, Weiming & Lin, Yezhi & Lin, Xiaolin, 2009. "The dynamical complexity of an impulsive Watt-type prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 731-744.
    6. Kim, Hye Kyung & Baek, Hunki, 2013. "The dynamical complexity of a predator–prey system with Hassell–Varley functional response and impulsive effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 1-14.
    7. Elettreby, M.F., 2009. "Two-prey one-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2018-2027.
    8. Tian, Yuan & Gao, Yan & Sun, Kaibiao, 2022. "Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    9. Zhao, Jiantao & Wei, Junjie, 2009. "Stability and bifurcation in a two harmful phytoplankton–zooplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1395-1409.
    10. Stamov, Gani Tr. & Simeonov, Stanislav & Stamova, Ivanka M., 2018. "Uncertain impulsive Lotka–Volterra competitive systems: Robust stability of almost periodic solutions," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 178-184.
    11. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2392-2404.
    12. Wang, Weiming & Wang, Xiaoqin & Lin, Yezhi, 2008. "Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1427-1441.
    13. Wang, Weiming & Wang, Hailing & Li, Zhenqing, 2008. "Chaotic behavior of a three-species Beddington-type system with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 438-443.
    14. Tian, Yuan & Li, Chunxue & Liu, Jing, 2023. "Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    15. Huo, Liang’an & Jiang, Jiehui & Gong, Sixing & He, Bing, 2016. "Dynamical behavior of a rumor transmission model with Holling-type II functional response in emergency event," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 228-240.
    16. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a periodic Watt-type predator–prey system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1270-1282.
    17. Xinmiao An & Xiaomin Wang & Boyu Zhang, 2020. "Bimatrix Replicator Dynamics with Periodic Impulses," Dynamic Games and Applications, Springer, vol. 10(3), pages 676-694, September.
    18. Wang, Weiming & Wang, Hailing & Li, Zhenqing, 2007. "The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1772-1785.
    19. Li, Zhenqing & Wang, Weiming & Wang, Hailing, 2006. "The dynamics of a Beddington-type system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1229-1239.
    20. Haidong Liu & Fanwei Meng, 2015. "Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, February.

    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:eee:chsofr:v:41:y:2009:i:4:p:1572-1577. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.