IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n952840.html

Stability and Dynamical Analysis of a Biological System

Author

Listed:
  • Xinhong Pan
  • Min Zhao
  • Yapei Wang
  • Hengguo Yu
  • Zengling Ma
  • Qi Wang

Abstract

This study considers the spatiotemporal dynamics of a reaction‐diffusion phytoplankton‐zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton.

Suggested Citation

  • Xinhong Pan & Min Zhao & Yapei Wang & Hengguo Yu & Zengling Ma & Qi Wang, 2014. "Stability and Dynamical Analysis of a Biological System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:952840
    DOI: 10.1155/2014/952840
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/952840
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/952840?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. Yanuo Zhu & Yongli Cai & Shuling Yan & Weiming Wang, 2012. "Dynamical Analysis of a Delayed Reaction-Diffusion Predator-Prey System," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-23, October.
    2. Edward R. Abraham, 1998. "The generation of plankton patchiness by turbulent stirring," Nature, Nature, vol. 391(6667), pages 577-580, February.
    3. R. Bhattacharyya & B. Mukhopadhyay, 2007. "Modeling Fluctuations In A Minimal Plankton Model: Role Of Spatial Heterogeneity And Stochasticity," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 197-216.
    4. Yanuo Zhu & Yongli Cai & Shuling Yan & Weiming Wang, 2012. "Dynamical Analysis of a Delayed Reaction‐Diffusion Predator‐Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    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. Nan Wang & Min Zhao & Hengguo Yu & Chuanjun Dai & Beibei Wang & Pengfei Wang, 2016. "Bifurcation Behavior Analysis in a Predator‐Prey Model," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

    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. Weifang Yan & Rui Liu, 2013. "Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time‐Delayed Degenerate Diffusion Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. 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).
    3. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2014. "Stability and Hopf Bifurcation Analysis of a Nutrient‐Phytoplankton Model with Delay Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Xinze Lian & Guichen Lu & Hailing Wang, 2014. "Pattern Formation in a Bacterial Colony Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Huang, Tousheng & Yu, Chengfeng & Zhang, Kui & Liu, Xingyu & Zhen, Jiulong & Wang, Lan, 2023. "Complex pattern dynamics and synchronization in a coupled spatiotemporal plankton system with zooplankton vertical migration," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    6. Suresh, R. & Senthilkumar, D.V. & Lakshmanan, M. & Kurths, J., 2016. "Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 235-245.
    7. Patrick Clifton Gray & Emmanuel Boss & Guillaume Bourdin & Yoav Lehahn, 2025. "Emergent patterns of patchiness differ between physical and planktonic properties in the ocean," Nature Communications, Nature, vol. 16(1), pages 1-12, December.
    8. Wang, Ching-Hao & Matin, Sakib & George, Ashish B. & Korolev, Kirill S., 2019. "Pinned, locked, pushed, and pulled traveling waves in structured environments," Theoretical Population Biology, Elsevier, vol. 127(C), pages 102-119.
    9. Enrico Ser-Giacomi & Ricardo Martinez-Garcia & Stephanie Dutkiewicz & Michael J. Follows, 2023. "A Lagrangian model for drifting ecosystems reveals heterogeneity-driven enhancement of marine plankton blooms," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    10. Das, Tanaya & Chakraborti, Saranya & Mukherjee, Joydeep & Sen, Goutam Kumar, 2018. "Mathematical modelling for phytoplankton distribution in Sundarbans Estuarine System, India," Ecological Modelling, Elsevier, vol. 368(C), pages 111-120.
    11. Evgeniya Giricheva, 2024. "Taxis-Driven Pattern Formation in Tri-Trophic Food Chain Model with Omnivory," Mathematics, MDPI, vol. 12(2), pages 1-18, January.
    12. Della Rossa, Fabio & Fasani, Stefano & Rinaldi, Sergio, 2013. "Conditions for patchiness in plankton models," Theoretical Population Biology, Elsevier, vol. 83(C), pages 95-100.
    13. Vilar, J.M.G. & Solé, R.V. & Rubı́, J.M., 2003. "On the origin of plankton patchiness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 239-246.
    14. Bengfort, Michael & Malchow, Horst, 2016. "Vertical mixing and hysteresis in the competition of buoyant and non-buoyant plankton prey species in a shallow lake," Ecological Modelling, Elsevier, vol. 323(C), pages 51-60.
    15. Serizawa, H. & Amemiya, T. & Itoh, K., 2009. "Patchiness and bistability in the comprehensive cyanobacterial model (CCM)," Ecological Modelling, Elsevier, vol. 220(6), pages 764-773.
    16. Joydev Chattopadhyay & Ezio Venturino & Samrat Chatterjee, 2013. "Aggregation of toxin-producing phytoplankton acts as a defence mechanism – a model-based study," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 19(2), pages 159-174, April.
    17. Ghorai, Santu & Chakraborty, Bhaskar & Bairagi, Nandadulal, 2021. "Preferential selection of zooplankton and emergence of spatiotemporal patterns in plankton population," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    18. Upadhyay, Ranjit Kumar & Kumari, Nitu & Rai, Vikas, 2009. "Wave of chaos in a diffusive system: Generating realistic patterns of patchiness in plankton–fish dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 262-276.

    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:jnlaaa:v:2014:y:2014:i:1:n:952840. 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/4058 .

    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.