IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2016y2016i1n9268257.html

Impulsive Control on Seasonally Perturbed General Holling Type Two‐Prey One‐Predator Model

Author

Listed:
  • Chandrima Banerjee
  • Pritha Das

Abstract

We investigate the dynamical behaviors of two‐prey one‐predator model with general Holling type functional responses. The effect of seasonal perturbation on the model has been discussed analytically as well as numerically. The periodic fluctuation is considered in prey growth rate and the predator mortality rate of the model. The impulsive effects involving biological and chemical control strategy, periodic releasing of natural enemies, and spraying pesticide at different fixed times are introduced in the model with seasonal perturbation. We derive the conditions of stability for impulsive system using Floquet theory, small amplitude perturbation skills. A local asymptotically stable prey (pest) eradicated periodic solution is obtained when the impulsive period is less than some critical value. Numerical simulations of the model with and without seasonal disturbances exhibit different dynamics. Also we simulate numerically the model involving seasonal perturbations without impulse and with impulse. Finally, concluding remarks are given.

Suggested Citation

  • Chandrima Banerjee & Pritha Das, 2016. "Impulsive Control on Seasonally Perturbed General Holling Type Two‐Prey One‐Predator Model," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:9268257
    DOI: 10.1155/2016/9268257
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2016/9268257
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/9268257?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. Chuanjun Dai & Min Zhao & Lansun Chen, 2013. "Bifurcations and Periodic Solutions for an Algae‐Fish Semicontinuous System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Tiancai Liao & Hengguo Yu & Chuanjun Dai & Min Zhao, 2019. "Impact of Cell Size Effect on Nutrient-Phytoplankton Dynamics," Complexity, Hindawi, vol. 2019, pages 1-23, November.
    3. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2015. "Dynamic Analysis of a Delayed Reaction‐Diffusion Predator‐Prey System with Modified Holling‐Tanner Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

    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:wly:jnddns:v:2016:y:2016:i:1:n:9268257. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3059 .

    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.