IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i4p1609-1615.html
   My bibliography  Save this article

Analysis of a Beddington–DeAngelis food chain chemostat with periodically varying dilution rate

Author

Listed:
  • Wang, Fengyan
  • Pang, Guoping
  • Lu, Zhengyi

Abstract

A model of a Beddington–DeAngelis type food chain chemostat with periodically varying dilution rate is considered. The system consists of one predator, one prey and limiting substrate. The periodic solutions of the subsystem with substrate and prey, which are the boundary periodic solutions of the system, are obtained. The stability analysis of the boundary periodic solution yields a predator invasion threshold. Above this threshold, there are periodic oscillations in the system. Furthermore, a model with sinusoidal dilution rate is numerically simulated. By bifurcation diagrams with different bifurcation parameters, the periodic system shows two kinds of bifurcations, whose are period-doubling and period-halving.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1609-1615
    DOI: 10.1016/j.chaos.2007.09.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907007813
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.09.041?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 & 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.
    5. Wang, Fengyan & Zhang, Shuwen & Chen, Lansun & Sun, Lihua, 2006. "Bifurcation and complexity of Monod type predator–prey system in a pulsed chemostat," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 447-458.
    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. 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.
    2. 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, 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Jiang, Guirong & Yang, Qigui, 2009. "Complex dynamics in a linear impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2341-2353.
    7. 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.
    8. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2009. "Extinction and permanence in delayed stage-structure predator–prey system with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2216-2224.
    9. Wang, Fengyan & Pang, Guoping, 2008. "Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1366-1376.
    10. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    11. Gan, Qintao & Xu, Rui & Yang, Pinghua, 2009. "Bifurcation and chaos in a ratio-dependent predator–prey system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1883-1895.
    12. Wang, Fengyan & Zeng, Guangzhao, 2007. "Chaos in a Lotka–Volterra predator–prey system with periodically impulsive ratio-harvesting the prey and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1499-1512.
    13. 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.
    14. Toth, Damon J.A., 2008. "Strong resonance and chaos in a single-species chemostat model with periodic pulsing of resource," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 55-69.

    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:40:y:2009:i:4:p:1609-1615. 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.