IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2016y2016i1n2560195.html

Dynamics of a Seasonally Forced Phytoplankton‐Zooplankton Model with Impulsive Biological Control

Author

Listed:
  • Jianglin Zhao
  • Yong Yan

Abstract

This paper investigates the dynamics of a seasonally forced phytoplankton‐zooplankton model with impulsive biological control. It shows that the periodic eradicated solution is unstable. Further, the condition for permanence of the system is established by relations between the model parameters and the intensity of the impulses. The numerical analysis is performed to study the effect of seasonality and impulsive perturbations on plankton dynamics. The numerical results imply that the seasonal forcing can trigger more periodic mode and the impulsive period for control of the size of phytoplankton is more practicable to the system than the impulsive release of zooplankton. These conclusions provide a better understanding of controlling harmful algae blooms.

Suggested Citation

  • Jianglin Zhao & Yong Yan, 2016. "Dynamics of a Seasonally Forced Phytoplankton‐Zooplankton Model with Impulsive Biological Control," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:2560195
    DOI: 10.1155/2016/2560195
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2016/2560195
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/2560195?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. 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.
    2. Jin Yang & Min Zhao, 2012. "A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. David M. Karl & Edward A. Laws & Paul Morris & Peter J. leB. Williams & Steven Emerson, 2003. "Metabolic balance of the open sea," Nature, Nature, vol. 426(6962), pages 32-32, November.
    4. Jin Yang & Min Zhao, 2012. "A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, April.
    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. Min Zhao & Yanzhen Wang & Lansun Chen, 2012. "Dynamic Analysis of a Predator‐Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Weiwei Zhang & Min Zhao, 2013. "Dynamical Complexity of a Spatial Phytoplankton‐Zooplankton Model with an Alternative Prey and Refuge Effect," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Hai-Feng Huo & Zhan-Ping Ma & Chun-Ying Liu, 2009. "Persistence and Stability for a Generalized Leslie‐Gower Model with Stage Structure and Dispersal," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    4. Zou, Xiaoling & Li, Qingwei & Cao, Wenhao & Lv, Jingliang, 2023. "Thresholds and critical states for a stochastic predator–prey model with mixed functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 780-795.
    5. Xiao, Qizhen & Dai, Binxiang, 2015. "Dynamics of an impulsive predator–prey logistic population model with state-dependent," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 220-230.
    6. Guo, Hongjian & Chen, Lansun & Song, Xinyu, 2009. "Dynamic analysis of a kind of species control model concerning impulsively releasing pathogen and infective predator," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1326-1336.
    7. Zizhen Zhang & Huizhong Yang, 2013. "Hopf Bifurcation Control in a Delayed Predator‐Prey System with Prey Infection and Modified Leslie‐Gower Scheme," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. 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.

    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:2560195. 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.