IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v79y2009i10p2994-3008.html
   My bibliography  Save this article

Continuous and impulsive harvesting strategies in a stage-structured predator–prey model with time delay

Author

Listed:
  • Yongzhen, Pei
  • Changguo, Li
  • Lansun, Chen

Abstract

In this paper, the continuous and impulsive harvesting policies are considered in a predator–prey system with stage-structure. In the case in which a continuous harvesting is used, it is shown that the mature predator becomes extinct under appropriate conditions. In the case in which an impulsive harvesting is used, using the discrete dynamical system determined by the stroboscopic map, we obtain the mature predator-eradication periodic solution of the system which is globally attractive. The conditions of permanence are established by the method of comparison involving multiple Liapunov functions and auxiliary function. These results indicate that: a short period of pulse harvest is a sufficient condition for the eradication of the population; the impulsive harvest policy is more effective than the continuous one from eradicating predator point of view. Our results offer a more economical and safe strategy in controlling pest in contrast with biological control and chemical control. Furthermore, we give a summary of the dynamic behavior when the impulsive period takes values in different intervals. Finally, numerical results show that the impulsive system we considered has more complex dynamics including quasi-periodic oscillation and chaos.

Suggested Citation

  • Yongzhen, Pei & Changguo, Li & Lansun, Chen, 2009. "Continuous and impulsive harvesting strategies in a stage-structured predator–prey model with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 2994-3008.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:10:p:2994-3008
    DOI: 10.1016/j.matcom.2009.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847540900007X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2009.01.003?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pandey, Soumik & Ghosh, Uttam & Das, Debashis & Chakraborty, Sarbani & Sarkar, Abhijit, 2024. "Rich dynamics of a delay-induced stage-structure prey–predator model with cooperative behaviour in both species and the impact of prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 49-76.
    2. Maiti, Atasi Patra & Dubey, B. & Chakraborty, A., 2019. "Global analysis of a delayed stage structure prey–predator model with Crowley–Martin type functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 58-84.
    3. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    4. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.

    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:matcom:v:79:y:2009:i:10:p:2994-3008. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.