IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i5p2812-2819.html
   My bibliography  Save this article

Dynamics of a three-species food chain model with adaptive traits

Author

Listed:
  • Sun, Chengjun
  • Loreau, Michel

Abstract

A three-species food chain model is proposed with dynamically variable adaptive traits in the intermediate consumer. We prove that its solutions are non-negative and bounded, and we analyze the existence and stability of its equilibria. By applying Li and Muldowney’s [Li MY, Muldowney J. On Bendixson’s criterion. J Differ Equ 1993;106:27–39] high-dimensional Bendixson criterion, we show that the positive equilibrium is globally stable under specific conditions. We support our analytical findings with numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2812-2819
    DOI: 10.1016/j.chaos.2008.10.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908004840
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.10.015?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 & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    2. Gakkhar, Sunita & Singh, Brahampal, 2007. "The dynamics of a food web consisting of two preys and a harvesting predator," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1346-1356.
    3. Gomes, A.A. & Manica, E. & Varriale, M.C., 2008. "Applications of chaos control techniques to a three-species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 432-441.
    4. Sun, Chengjun & Han, Maoan & Lin, Yiping & Chen, Yuanyuan, 2007. "Global qualitative analysis for a predator–prey system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1582-1596.
    5. Chen, Yuanyuan & Yu, Jiang & Sun, Chengjun, 2007. "Stability and Hopf bifurcation analysis in a three-level food chain system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 683-694.
    6. 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.
    7. Gomes, A.A. & Manica, E. & Varriale, M.C., 2008. "Applications of chaos control techniques to a three-species food chain," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 1097-1107.
    Full references (including those not matched with items on IDEAS)

    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. Zhao, Min & Yu, Hengguo & Zhu, Jun, 2009. "Effects of a population floor on the persistence of chaos in a mutual interference host–parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1245-1250.
    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. 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.
    13. 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.
    14. 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.
    15. Swarnali Sharma & G. P. Samanta, 2013. "Mathematical Analysis of a Single-Species Population Model in a Polluted Environment with Discrete Time Delays," Journal of Mathematics, Hindawi, vol. 2013, pages 1-18, June.
    16. 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.
    17. 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.
    18. 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.
    19. Chen, Yuanyuan & Changming, Song, 2008. "Stability and Hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1104-1114.
    20. Pal, D. & Mahapatra, G.S., 2016. "Effect of toxic substance on delayed competitive allelopathic phytoplankton system with varying parameters through stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 109-124.

    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:5:p:2812-2819. 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.