IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2911-d1182208.html
   My bibliography  Save this article

Stability and Bifurcations in a Nutrient–Phytoplankton–Zooplankton Model with Delayed Nutrient Recycling with Gamma Distribution

Author

Listed:
  • Mihaela Sterpu

    (Department of Mathematics, University of Craiova, 200585 Craiova, Romania)

  • Carmen Rocşoreanu

    (Department of Statistics and Economic Informatics, University of Craiova, 200585 Craiova, Romania)

  • Raluca Efrem

    (Department of Mathematics, University of Craiova, 200585 Craiova, Romania)

  • Sue Ann Campbell

    (Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada)

Abstract

Two nutrient–phytoplankton–zooplankton (NZP) models for a closed ecosystem that incorporates a delay in nutrient recycling, obtained using the gamma distribution function with one or two degrees of freedom, are analysed. The models are described by systems of ordinary differential equations of four and five dimensions. The purpose of this study is to investigate how the mean delay of the distribution and the total nutrients affect the stability of the equilibrium solutions. Local stability theory and bifurcation theory are used to determine the long-time dynamics of the models. It is found that both models exhibit comparable qualitative dynamics. There are a maximum of three equilibrium points in each of the two models, and at most one of them is locally asymptotically stable. The change of stability from one equilibrium to another takes place through a transcritical bifurcation. In some hypotheses on the functional response, the nutrient–phytoplankton–zooplankton equilibrium loses stability via a supercritical Hopf bifurcation, causing the apparition of a stable limit cycle. The way in which the results are consistent with prior research and how they extend them is discussed. Finally, various application-related consequences of the results of the theoretical study are deduced.

Suggested Citation

  • Mihaela Sterpu & Carmen Rocşoreanu & Raluca Efrem & Sue Ann Campbell, 2023. "Stability and Bifurcations in a Nutrient–Phytoplankton–Zooplankton Model with Delayed Nutrient Recycling with Gamma Distribution," Mathematics, MDPI, vol. 11(13), pages 1-24, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2911-:d:1182208
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2911/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2911/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Samarpita Basu & Katherine R. M. Mackey, 2018. "Phytoplankton as Key Mediators of the Biological Carbon Pump: Their Responses to a Changing Climate," Sustainability, MDPI, vol. 10(3), pages 1-18, March.
    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. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
    2. Vincent Bian & Merrick Cai & Christopher L. Follett, 2023. "Understanding opposing predictions of Prochlorococcus in a changing climate," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    3. Teng Li & Yan Bai & Xianqiang He & Xiaoyan Chen & Chen-Tung Arthur Chen & Bangyi Tao & Delu Pan & Xuan Zhang, 2018. "The Relationship between POC Export Efficiency and Primary Production: Opposite on the Shelf and Basin of the Northern South China Sea," Sustainability, MDPI, vol. 10(10), pages 1-22, October.
    4. Samarpita Basu & Katherine R. M. Mackey, 2022. "Effect of Rising Temperature and Carbon Dioxide on the Growth, Photophysiology, and Elemental Ratios of Marine Synechococcus : A Multistressor Approach," Sustainability, MDPI, vol. 14(15), pages 1-21, August.
    5. Charissa M. Ferrera & Gil S. Jacinto & Chen-Tung Arthur Chen & Hon-Kit Lui, 2018. "Organic Carbon Concentrations in High- and Low-Productivity Areas of the Sulu Sea," Sustainability, MDPI, vol. 10(6), pages 1-19, June.
    6. Heneghan, Ryan F. & Everett, Jason D. & Sykes, Patrick & Batten, Sonia D. & Edwards, Martin & Takahashi, Kunio & Suthers, Iain M. & Blanchard, Julia L. & Richardson, Anthony J., 2020. "A functional size-spectrum model of the global marine ecosystem that resolves zooplankton composition," Ecological Modelling, Elsevier, vol. 435(C).
    7. Heike H. Zimmermann & Kathleen R. Stoof-Leichsenring & Viktor Dinkel & Lars Harms & Luise Schulte & Marc-Thorsten Hütt & Dirk Nürnberg & Ralf Tiedemann & Ulrike Herzschuh, 2023. "Marine ecosystem shifts with deglacial sea-ice loss inferred from ancient DNA shotgun sequencing," Nature Communications, Nature, vol. 14(1), pages 1-13, December.

    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:gam:jmathe:v:11:y:2023:i:13:p:2911-:d:1182208. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.