IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v29y2006i2p474-482.html
   My bibliography  Save this article

Chaotic behavior of a chemostat model with Beddington–DeAngelis functional response and periodically impulsive invasion

Author

Listed:
  • Zhang, Shuwen
  • Tan, Dejun
  • Chen, Lansun

Abstract

In the paper, we considered a predator–prey model with Beddington–DeAngelis functional response in periodic pulsed chemostat. We discussed the boundness of system and the stability of prey and predator-eradication periodic solution of system. Further, using numerical simulation method, we show that this impulsive system with periodically pulsed substrate display a series of complex phenomena, which include (1) period-doubling cascade, (2) period-halfing cascade, (3) chaos and (4) periodic window.

Suggested Citation

  • Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaotic behavior of a chemostat model with Beddington–DeAngelis functional response and periodically impulsive invasion," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 474-482.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:474-482
    DOI: 10.1016/j.chaos.2005.08.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905006806
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.08.026?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 & Wang, Fengyan & Chen, Lansun, 2005. "A food chain model with impulsive perturbations and Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 855-866.
    2. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    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. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    2. Li, Wan-Tong & Wu, Shi-Liang, 2008. "Traveling waves in a diffusive predator–prey model with holling type-III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 476-486.
    3. San Martín, Jesús & Moscoso, Ma José & González Gómez, A., 2009. "The universal cardinal ordering of fixed points," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1996-2007.
    4. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    5. Wu, Shi-Liang & Li, Wan-Tong, 2009. "Global asymptotic stability of bistable traveling fronts in reaction-diffusion systems and their applications to biological models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1229-1239.
    6. Kang, Li & Tang, Sanyi, 2016. "The reverse effects of random perturbation on discrete systems for single and multiple population models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 198-209.

    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. 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.
    3. 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.
    4. 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.
    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. Sun, Chengjun & Loreau, Michel, 2009. "Dynamics of a three-species food chain model with adaptive traits," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2812-2819.
    7. 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.
    8. Guo, Hongjian & Song, Xinyu, 2008. "An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1320-1331.
    9. 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.
    10. Yongzhen, Pei & Yong, Yang & Changguo, Li, 2009. "Dynamics of an impulsive control system which prey species share a common predator," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2429-2436.
    11. Han, Xinli & Teng, Zhidong & Xiao, Dongmei, 2006. "Persistence and average persistence of a nonautonomous Kolmogorov system," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 748-758.
    12. 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.
    13. 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.
    14. Zhou, Can & Fujiwara, Masami & Grant, William E., 2013. "Dynamics of a predator–prey interaction with seasonal reproduction and continuous predation," Ecological Modelling, Elsevier, vol. 268(C), pages 25-36.

    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:29:y:2006:i:2:p:474-482. 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.