IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4808-d1289753.html
   My bibliography  Save this article

Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay

Author

Listed:
  • Qingyi Cui

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Changjin Xu

    (Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Wei Ou

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Yicheng Pang

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Zixin Liu

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Peiluan Li

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Lingyun Yao

    (Library, Guizhou University of Finance and Economics, Guiyang 550025, China)

Abstract

All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed point theorem, inequality tactics and an appropriate function, we gain the sufficient criteria on existence and uniqueness, non-negativeness and boundedness of the solution to the formulated delayed Lotka–Volterra commensal symbiosis system. Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. A new delay-independent stability and bifurcation conditions on the model are presented. By constructing a positive definite function, we explore the global stability. By constructing two diverse hybrid delayed feedback controllers, we can adjusted the domain of stability and time of appearance of Hopf bifurcation of the delayed Lotka–Volterra commensal symbiosis system. The effect of time delay on the domain of stability and time of appearance of Hopf bifurcation of the model is given. Matlab experiment diagrams are provided to sustain the acquired key outcomes.

Suggested Citation

  • Qingyi Cui & Changjin Xu & Wei Ou & Yicheng Pang & Zixin Liu & Peiluan Li & Lingyun Yao, 2023. "Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay," Mathematics, MDPI, vol. 11(23), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4808-:d:1289753
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4808/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4808/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li, Shuai & Huang, Chengdai & Song, Xinyu, 2023. "Detection of Hopf bifurcations induced by pregnancy and maturation delays in a spatial predator–prey model via crossing curves method," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Feng, Xiaozhou & Liu, Xia & Sun, Cong & Jiang, Yaolin, 2023. "Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Garai, Shilpa & Pati, N.C. & Pal, Nikhil & Layek, G.C., 2022. "Organized periodic structures and coexistence of triple attractors in a predator–prey model with fear and refuge," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Liang, Ziwei & Meng, Xinyou, 2023. "Stability and Hopf bifurcation of a multiple delayed predator–prey system with fear effect, prey refuge and Crowley–Martin function," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    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. Zhang, Huayong & Guo, Fenglu & Zou, Hengchao & Zhao, Lei & Wang, Zhongyu & Yuan, Xiaotong & Liu, Zhao, 2024. "Refuge-driven spatiotemporal chaos in a discrete predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    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. Qiuyue Zhao & Xinglong Niu, 2024. "Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    2. Kumbhakar, Ruma & Hossain, Mainul & Karmakar, Sarbari & Pal, Nikhil, 2024. "An investigation of the parameter space in a tri-trophic food chain model with refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 37-59.
    3. Haoming Shi & Fei Xu & Jinfu Cheng & Victor Shi, 2023. "Exploring the Evolution of the Food Chain under Environmental Pollution with Mathematical Modeling and Numerical Simulation," Sustainability, MDPI, vol. 15(13), pages 1-17, June.
    4. Abbasi, Muhammad Aqib & Samreen, Maria, 2024. "Analyzing multi-parameter bifurcation on a prey–predator model with the Allee effect and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    5. Li, Shuai & Cao, Jinde & Liu, Heng & Huang, Chengdai, 2024. "Delay-dependent parameters bifurcation in a fractional neural network via geometric methods," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    6. Dipesh Barman & Ranjit Kumar Upadhyay, 2023. "Modelling Predator–Prey Interactions: A Trade-Off between Seasonality and Wind Speed," Mathematics, MDPI, vol. 11(23), pages 1-26, 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:23:p:4808-:d:1289753. 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.