IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v163y2022ics0960077922007305.html
   My bibliography  Save this article

Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses

Author

Listed:
  • Liang, Yuqin
  • Jia, Yunfeng

Abstract

In this paper, we deal with a plankton reaction–diffusion model with time-delay and two different functional responses. Firstly, we consider the global stability of boundary equilibrium point. Secondly, we investigate the existence, uniqueness and stability of internal equilibrium point without time-delay. Then, we analyze the existence of Hopf bifurcation emitting from internal equilibrium point and give some characteristics on Hopf branch in detail. A new finding is presented, specifically, we find that there exist two critical values which have important effects on the occurrence of Hopf bifurcation. Finally, a few numerical examples are presented to check and illustrate the theoretical analysis, some simulation graphs, including the spatiotemporal graphs, trajectory graphs and phase portraits are depicted graphically.

Suggested Citation

  • Liang, Yuqin & Jia, Yunfeng, 2022. "Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007305
    DOI: 10.1016/j.chaos.2022.112533
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922007305
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112533?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. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Jia, Yunfeng, 2020. "Bifurcation and pattern formation of a tumor–immune model with time-delay and diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 92-108.
    3. Liu, Zhi-bin & Liu, Shu-tang & Tian, Da-dong & Wang, Da, 2021. "Stability analysis of the plankton community with advection," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Wen, Shao-Fang & Shen, Yong-Jun & Yang, Shao-Pu & Wang, Jun, 2017. "Dynamical response of Mathieu–Duffing oscillator with fractional-order delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 54-62.
    5. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    6. Zhao, Hongyong & Huang, Xuanxuan & Zhang, Xuebing, 2015. "Hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 300-315.
    7. Wang, Jingjing & Zheng, Hongchan & Jia, Yunfeng, 2021. "Dynamical analysis on a bacteria-phages model with delay and diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
    9. Jiang, Zhichao & Zhang, Tongqian, 2017. "Dynamical analysis of a reaction-diffusion phytoplankton-zooplankton system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 693-704.
    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. 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).
    2. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    3. Ahmed Alsaedi & Amjad F. Albideewi & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions," Mathematics, MDPI, vol. 8(11), pages 1-14, October.
    4. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Spatial dynamics of a fractional predator-prey system with time delay and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Wafaa S. Sayed & Moheb M. R. Henein & Salwa K. Abd-El-Hafiz & Ahmed G. Radwan, 2017. "Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems," Complexity, Hindawi, vol. 2017, pages 1-17, February.
    6. Bashir Ahmad & Madeaha Alghanmi & Ahmed Alsaedi & Hari M. Srivastava & Sotiris K. Ntouyas, 2019. "The Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral," Mathematics, MDPI, vol. 7(6), pages 1-10, June.
    7. Fatmawati, & Khan, Muhammad Altaf & Azizah, Muftiyatul & Windarto, & Ullah, Saif, 2019. "A fractional model for the dynamics of competition between commercial and rural banks in Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 32-46.
    8. 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.
    9. Ahmed Alsaedi & Bashir Ahmad & Madeaha Alghanmi & Sotiris K. Ntouyas, 2019. "On a Generalized Langevin Type Nonlocal Fractional Integral Multivalued Problem," Mathematics, MDPI, vol. 7(11), pages 1-13, October.
    10. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    11. Yifan Zhang & Tianzeng Li & Zhiming Zhang & Yu Wang, 2022. "Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes," Mathematics, MDPI, vol. 10(11), pages 1-22, June.
    12. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2020. "Delay induced nonlinear dynamics of oxygen-plankton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    13. Oliveira, José J., 2022. "Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    14. Liu, Q.X. & Liu, J.K. & Chen, Y.M., 2017. "An analytical criterion for jump phenomena in fractional Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 216-219.
    15. Kingni, Sifeu Takougang & Pham, Viet-Thanh & Jafari, Sajad & Woafo, Paul, 2017. "A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 209-218.
    16. Fiaz, Muhammad & Aqeel, Muhammad & Marwan, Muhammad & Sabir, Muhammad, 2022. "Integer and fractional order analysis of a 3D system and generalization of synchronization for a class of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    17. Michal Fečkan & T. Sathiyaraj & JinRong Wang, 2020. "Synchronization of Butterfly Fractional Order Chaotic System," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    18. Amine, Saida & Hajri, Youssra & Allali, Karam, 2022. "A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    19. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong, 2019. "Chaotic analysis and adaptive synchronization for a class of fractional order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 33-42.
    20. Chuanjun Dai & Hengguo Yu & Qing Guo & He Liu & Qi Wang & Zengling Ma & Min Zhao, 2019. "Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-16, February.

    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:163:y:2022:i:c:s0960077922007305. 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.