IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v154y2022ics0960077921009711.html
   My bibliography  Save this article

The impact of plankton body size on phytoplankton-zooplankton dynamics in the absence and presence of stochastic environmental fluctuation

Author

Listed:
  • Liao, Tiancai

Abstract

In this paper, we study the dynamics of a stochastic phytoplankton-zooplankton (PZ) model with phytoplankton cell size and zooplankton body size. In the case of PZ model without stochastic environmental fluctuations, we provide the positivity and boundedness of the solutions, investigate the dissipativity and permanence of the model, prove the existence of Hopf bifurcation, and give the local and global stability of the boundary and positive equilibria. In the case of PZ model with stochastic environmental fluctuations, the stochastic dynamics including a unique ergodic stationary distribution, stochastic permanence, stochastic extinction and persistence in the mean are explored in detail. Based on the theoretical analysis above, via numerical simulations, we find that the increase of environmental capacity can not only destabilize the deterministic model via Hopf bifurcation and induce periodic solutions, but can also stabilize the deterministic model by rejecting the periodic solutions. Interestingly, the increase of phytoplankton cell size or zooplankton body size can stabilize the deterministic model by excluding the periodic solutions induced by environmental capacity. Additionally, it is worth emphasizing that the small phytoplankton cell size can lead to the inability of plankton to survive in both deterministic and random environments, while the small zooplankton body size can destabilize the deterministic model and induce periodic solutions. Furthermore, it should be noted that the large phytoplankton cell size can weaken the effect of random environmental disturbance, but large zooplankton body size can not. These results may provide new insights in understanding the complex dynamics of phytoplankton-zooplankton models.

Suggested Citation

  • Liao, Tiancai, 2022. "The impact of plankton body size on phytoplankton-zooplankton dynamics in the absence and presence of stochastic environmental fluctuation," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009711
    DOI: 10.1016/j.chaos.2021.111617
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009711
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111617?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. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Oxygen-plankton model under the effect of global warming with nonsingular fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Jeff C. Ho & Anna M. Michalak & Nima Pahlevan, 2019. "Widespread global increase in intense lake phytoplankton blooms since the 1980s," Nature, Nature, vol. 574(7780), pages 667-670, October.
    4. Jang, Sophia R.-J. & Allen, Edward J., 2015. "Deterministic and stochastic nutrient-phytoplankton- zooplankton models with periodic toxin producing phytoplankton," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 52-67.
    5. Zhao, Qiuyue & Liu, Shutang & Niu, Xinglong, 2020. "Effect of water temperature on the dynamic behavior of phytoplankton–zooplankton model," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    6. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
    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. Liao, Tiancai, 2024. "The impact of temperature variation on the algae–zooplankton dynamics with size-selective disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Yassine Sabbar & Asad Khan & Anwarud Din, 2022. "Probabilistic Analysis of a Marine Ecological System with Intense Variability," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    3. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.

    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. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    2. Rao, Feng & Wang, Weiming & Li, Zhenqing, 2009. "Spatiotemporal complexity of a predator–prey system with the effect of noise and external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1634-1644.
    3. Bo Qin & Rong Wang & Xiangdong Yang & Qinghui Zhang & Jianan Zheng, 2023. "Reconstruction and Trends of Total Phosphorus in Shallow Lakes in Eastern China in The Past Century," Sustainability, MDPI, vol. 15(14), pages 1-15, July.
    4. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. repec:ags:aaea22:335506 is not listed on IDEAS
    6. Chun Zhang & Tao Yang & Shi-Xian Qu, 2021. "Impact of time delays and environmental noise on the extinction of a population dynamics model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-16, November.
    7. Zhang, Wenyue & Shi, Peiming & Li, Mengdi & Han, Dongying, 2021. "A novel stochastic resonance model based on bistable stochastic pooling network and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2019. "Stochastic variability and transitions to chaos in a hierarchical three-species population model," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 276-283.
    9. Alexander E. Cagle & Alona Armstrong & Giles Exley & Steven M. Grodsky & Jordan Macknick & John Sherwin & Rebecca R. Hernandez, 2020. "The Land Sparing, Water Surface Use Efficiency, and Water Surface Transformation of Floating Photovoltaic Solar Energy Installations," Sustainability, MDPI, vol. 12(19), pages 1-22, October.
    10. Lifan Chen & Xingwang Yu & Sanling Yuan, 2022. "Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    11. Aparicio, Genoveva & Camacho, Maximo & Maté-Sánchez-Val, Mariluz, 2024. "Quantifying the impact: Are coastal areas impoverished by marine pollution?," Ecological Economics, Elsevier, vol. 221(C).
    12. Ai, Hao & Yang, GuiJiang & Liu, Wei & Wang, Qiubao, 2023. "A fast search method for optimal parameters of stochastic resonance based on stochastic bifurcation and its application in fault diagnosis of rolling bearings," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    13. Liao, Tiancai, 2024. "The impact of temperature variation on the algae–zooplankton dynamics with size-selective disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    14. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    15. Changchun Peng & Zhijun Xie & Xing Jin, 2024. "Using Ensemble Learning for Remote Sensing Inversion of Water Quality Parameters in Poyang Lake," Sustainability, MDPI, vol. 16(8), pages 1-19, April.
    16. Chakraborty, Subhendu & Moorthi, Stefanie D. & Karnatak, Rajat & Feudel, Ulrike, 2022. "Irregular harmful algal blooms triggered by feedback between toxin production and zooplankton feeding," Ecological Modelling, Elsevier, vol. 473(C).
    17. Guo, Qing & Wang, Yi & Dai, Chuanjun & Wang, Lijun & Liu, He & Li, Jianbing & Tiwari, Pankaj Kumar & Zhao, Min, 2023. "Dynamics of a stochastic nutrient–plankton model with regime switching," Ecological Modelling, Elsevier, vol. 477(C).
    18. Akgül, Akif & Rajagopal, Karthikeyan & Durdu, Ali & Pala, Muhammed Ali & Boyraz, Ömer Faruk & Yildiz, Mustafa Zahid, 2021. "A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    19. Konstantinos Metaxoglou & Aaron Smith, 2022. "Nutrient Pollution and US Agriculture: Causal Effects, Integrated Assessment, and Implications of Climate Change," NBER Chapters, in: American Agriculture, Water Resources, and Climate Change, pages 297-341, National Bureau of Economic Research, Inc.
    20. Ratté-Fortin, Claudie & Chokmani, Karem & El Alem, Anas & Laurion, Isabelle, 2022. "A regional model to predict the occurrence of natural events: Application to phytoplankton blooms in continental waterbodies," Ecological Modelling, Elsevier, vol. 473(C).
    21. Kuşkaya, Sevda, 2022. "Residential solar energy consumption and greenhouse gas nexus: Evidence from Morlet wavelet transforms," Renewable Energy, Elsevier, vol. 192(C), pages 793-804.

    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:154:y:2022:i:c:s0960077921009711. 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.