IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i2p778-785.html
   My bibliography  Save this article

The global stability of a delayed predator–prey system with two stage-structure

Author

Listed:
  • Wang, Fengyan
  • Pang, Guoping

Abstract

Based on the classical delayed stage-structured model and Lotka–Volterra predator–prey model, we introduce and study a delayed predator–prey system, where prey and predator have two stages, an immature stage and a mature stage. The time delays are the time lengths between the immature’s birth and maturity of prey and predator species. Results on global asymptotic stability of nonnegative equilibria of the delay system are given, which generalize and suggest that good continuity exists between the predator–prey system and its corresponding stage-structured system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:778-785
    DOI: 10.1016/j.chaos.2007.08.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907006364
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.08.024?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. Gao, Shujing & Chen, Lansun & Sun, Lihua, 2005. "Optimal pulse fishing policy in stage-structured models with birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1209-1219.
    2. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
    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. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Gu, En-Guo & Hao, Yu-Dong, 2007. "On the global analysis of dynamics in a delayed regulation model with an external interference," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1272-1284.
    5. Gao, Shujing & Chen, Lansun & Sun, Lihua, 2005. "Dynamic complexities in a seasonal prevention epidemic model with birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1171-1181.
    6. Zhao, Hongyong & Zhang, Xuebing & Huang, Xuanxuan, 2015. "Hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 462-480.
    7. Yun Liu & Lifeng Guo & Xijuan Liu, 2023. "Dynamical Behaviors in a Stage-Structured Model with a Birth Pulse," Mathematics, MDPI, vol. 11(15), pages 1-13, July.
    8. Çelik, C. & Merdan, H. & Duman, O. & Akın, Ö., 2008. "Allee effects on population dynamics with delay," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 65-74.
    9. Jiao, Jianjun & Chen, Lansun & Cai, Shaohong, 2009. "A delayed stage-structured Holling II predator–prey model with mutual interference and impulsive perturbations on predator," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1946-1955.
    10. Gao, Shujing & Chen, Lansun & Sun, Lihua, 2005. "Optimal pulse fishing policy in stage-structured models with birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1209-1219.
    11. Banerjee, Ritwick & Das, Pritha & Mukherjee, Debasis, 2018. "Stability and permanence of a discrete-time two-prey one-predator system with Holling Type-III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 240-248.
    12. Cui, Qianqian & Zhang, Qiang & Qiu, Zhipeng & Hu, Zengyun, 2016. "Complex dynamics of a discrete-time predator-prey system with Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 158-171.
    13. Gao, Shujing & Teng, Zhidong & Xie, Dehui, 2009. "Analysis of a delayed SIR epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1004-1011.
    14. Ahjond S. Garmestani & Craig R. Allen & Colin M. Gallagher & John D. Mittelstaedt, 2007. "Departures from Gibrat's Law, Discontinuities and City Size Distributions," Urban Studies, Urban Studies Journal Limited, vol. 44(10), pages 1997-2007, September.
    15. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    16. Terry, Alan J., 2015. "A population model with birth pulses, age structure, and non-overlapping generations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 400-417.
    17. Zhao, Hongyong & Huang, Xuanxuan & Zhang, Xuebing, 2015. "Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 300-315.
    18. Xiang, Zhongyi & Song, Xinyu, 2007. "A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1419-1428.
    19. Merdan, H. & Duman, O. & Akın, Ö. & Çelik, C., 2009. "Allee effects on population dynamics in continuous (overlapping) case," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1994-2001.

    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:2:p:778-785. 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.