IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v36y2008i3p729-739.html
   My bibliography  Save this article

Boundedness and permanence in a class of periodic time-dependent predator–prey system with prey dispersal and predator density-independence

Author

Listed:
  • Zhang, Long
  • Teng, Zhidong

Abstract

In this paper, we study two species predator–prey Lotka–Volterra type dispersal system with periodic coefficients, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of the patches and cannot disperse. Sufficient conditions on the boundedness, permanence and existence of positive periodic solution for this system are established. The theoretical results are confirmed by a special example and numerical simulations.

Suggested Citation

  • Zhang, Long & Teng, Zhidong, 2008. "Boundedness and permanence in a class of periodic time-dependent predator–prey system with prey dispersal and predator density-independence," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 729-739.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:729-739
    DOI: 10.1016/j.chaos.2006.07.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906007089
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.07.003?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, Zhihua & Yuan, Rong, 2006. "Stability and bifurcation in a harvested one-predator–two-prey model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1395-1407.
    2. 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. Anatoliy Martynyuk & Gani Stamov & Ivanka Stamova & Ekaterina Gospodinova, 2023. "Formulation of Impulsive Ecological Systems Using the Conformable Calculus Approach: Qualitative Analysis," Mathematics, MDPI, vol. 11(10), pages 1-15, May.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Zhang, Xue & Zhang, Qing-Ling & Liu, Chao & Xiang, Zhong-Yi, 2009. "Bifurcations of a singular prey–predator economic model with time delay and stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1485-1494.
    9. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    10. 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.
    11. Jana, Soovoojeet & Ghorai, Abhijit & Guria, Srabani & Kar, T.K., 2015. "Global dynamics of a predator, weaker prey and stronger prey system," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 235-248.
    12. 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.
    13. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    14. Xu, Rui & Ma, Zhien, 2008. "Stability and Hopf bifurcation in a ratio-dependent predator–prey system with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 669-684.
    15. 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.
    16. 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.
    17. Zhang, Long & Teng, Zhidong, 2008. "Permanence for a class of periodic time-dependent predator–prey system with dispersal in a patchy-environment," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1483-1497.
    18. Agarwal, Ravi P. & Özbekler, Abdullah, 2016. "Lyapunov type inequalities for second order forced mixed nonlinear impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 216-225.
    19. Wang, Hailing & Wang, Weiming, 2008. "The dynamical complexity of a Ivlev-type prey–predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1168-1176.
    20. Cerqueti, Roy & Quaranta, Anna Grazia & Ventura, Marco, 2016. "Innovation, imitation and policy inaction," Technological Forecasting and Social Change, Elsevier, vol. 111(C), pages 22-30.

    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:36:y:2008:i:3:p:729-739. 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.