IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i5p2786-2795.html
   My bibliography  Save this article

Analysis of a Lotka–Volterra food chain chemostat with converting time delays

Author

Listed:
  • Wang, Fengyan
  • Pang, Guoping
  • Zhang, Shuwen

Abstract

A model of the food chain chemostat involving predator, prey and growth-limiting nutrients is considered. The model incorporates two discrete time delays in order to describe the time involved in converting processes. The Lotka–Volterra type increasing functions are used to describe the species uptakes. In addition to showing that solutions with positive initial conditions are positive and bounded, we establish sufficient conditions for the (i) local stability and instability of the positive equilibrium and (ii) global stability of the non-negative equilibria. Numerical simulation suggests that the delays have both destabilizing and stabilizing effects, and the system can produce stable periodic solutions, quasi-periodic solutions and strange attractors.

Suggested Citation

  • Wang, Fengyan & Pang, Guoping & Zhang, Shuwen, 2009. "Analysis of a Lotka–Volterra food chain chemostat with converting time delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2786-2795.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2786-2795
    DOI: 10.1016/j.chaos.2009.03.189
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909003464
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.03.189?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. Wang, Fengyan & Hao, Chunping & Chen, Lansun, 2007. "Bifurcation and chaos in a Monod type food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 826-839.
    2. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2008. "Analysis of a Monod–Haldene type food chain chemostat with periodically varying substrate," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 731-742.
    3. Wang, Fengyan & Hao, Chunping & Chen, Lansun, 2007. "Bifurcation and chaos in a Monod–Haldene type food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 181-194.
    4. Wang, Fengyan & Pang, Guoping & Lu, Zhengyi, 2009. "Analysis of a Beddington–DeAngelis food chain chemostat with periodically varying dilution rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1609-1615.
    5. Wang, Fengyan & Hao, Chunping & Chen, Lansun, 2007. "Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1547-1561.
    6. Wang, Fengyan & Pang, Guoping, 2009. "The global stability of a delayed predator–prey system with two stage-structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 778-785.
    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. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.

    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, Fengyan & Pang, Guoping & Lu, Zhengyi, 2009. "Analysis of a Beddington–DeAngelis food chain chemostat with periodically varying dilution rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1609-1615.
    2. Yu, Hengguo & Zhao, Min & Lv, Songjuan & Zhu, Lili, 2009. "Dynamic complexities in a parasitoid-host-parasitoid ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 39-48.
    3. Jiang, Guirong & Yang, Qigui, 2009. "Complex dynamics in a linear impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2341-2353.
    4. 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.
    5. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2008. "Analysis of a Monod–Haldene type food chain chemostat with periodically varying substrate," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 731-742.
    6. 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.
    7. Wang, Fengyan & Kuang, Yang & Ding, Changming & Zhang, Shuwen, 2013. "Stability and bifurcation of a stage-structured predator–prey model with both discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 19-27.
    8. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.

    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:42:y:2009:i:5:p:2786-2795. 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.