IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v166y2023ics0960077922011547.html
   My bibliography  Save this article

Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system

Author

Listed:
  • Li, Peiluan
  • Gao, Rong
  • Xu, Changjin
  • Li, Ying
  • Akgül, Ali
  • Baleanu, Dumitru

Abstract

In this study, we are concerned with the dynamics of a new established fractional-order delayed zooplankton–phytoplankton system. The existence and uniqueness of the solution are proved via Banach fixed point theorem. Non-negativeness of the solution is studied by mathematical inequality technique. The boundedness of the solution is analyzed by virtue of constructing an appropriate function. A novel delay-independent sufficient condition ensuring the stability and the onset of Hopf bifurcation for the established fractional-order delayed zooplankton–phytoplankton system is derived by means of Laplace transform, stability criterion and bifurcation knowledge of fractional-order differential equation. The global stability condition for the involved fractional-order delayed zooplankton–phytoplankton system is built by using a suitable positive definite function. Taking advantage of hybrid control tactics, we effectively control the time of occurrence of Hopf bifurcation for the established fractional-order delayed zooplankton–phytoplankton system. The study manifests that delay plays a vital role in controlling the stability and the time of occurrence of Hopf bifurcation for the involved fractional-order delayed zooplankton–phytoplankton system and the fractional-order controlled zooplankton–phytoplankton system involving delays. To verify the correctness of established chief results, computer simulation figures are distinctly displayed. The derived conclusions of this research are entirely new and possess potential theoretical value in preserving the balance of biological population. Up to now, there are few publications on detailed and comprehensive dynamic analysis on fractional-order delayed zooplankton–phytoplankton system via various exploration ways.

Suggested Citation

  • Li, Peiluan & Gao, Rong & Xu, Changjin & Li, Ying & Akgül, Ali & Baleanu, Dumitru, 2023. "Dynamics exploration for a fractional-order delayed zooplankton–phytoplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011547
    DOI: 10.1016/j.chaos.2022.112975
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922011547
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112975?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. Al-Nassir, Sadiq, 2021. "Dynamic analysis of a harvested fractional-order biological system with its discretization," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Huang, Conggui & Wang, Fei & Zheng, Zhaowen, 2021. "Exponential stability for nonlinear fractional order sampled-data control systems with its applications," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    4. Anitha Karthikeyan & Karthikeyan Rajagopal & Victor Kamdoum Tamba & Girma Adam & Ashokkumar Srinivasan & Chun-Biao Li, 2021. "A Simple Chaotic Wien Bridge Oscillator with a Fractional-Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability," Complexity, Hindawi, vol. 2021, pages 1-13, March.
    5. Ma, Tingting & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2021. "Stability analysis and optimal harvesting control of a cross-diffusion prey-predator system," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Zhao, Qiuyue & Liu, Shutang & Tian, Dadong, 2018. "Dynamic behavior analysis of phytoplankton–zooplankton system with cell size and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 160-168.
    7. Iyiola, Olaniyi & Oduro, Bismark & Akinyemi, Lanre, 2021. "Analysis and solutions of generalized Chagas vectors re-infestation model of fractional order type," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. 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).
    9. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    10. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.
    11. Agnihotri, Kulbhushan & Kaur, Harpreet, 2021. "Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 946-964.
    12. 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.
    13. Duc, Tran Minh & Van Hoa, Ngo, 2021. "Stabilization of impulsive fractional-order dynamic systems involving the Caputo fractional derivative of variable-order via a linear feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    14. Xu, Changjin & Liu, Zixin & Yao, Lingyun & Aouiti, Chaouki, 2021. "Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    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. Xu, Changjin & Farman, Muhammad, 2023. "Qualitative and Ulam–Hyres stability analysis of fractional order cancer-immune model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. He, Ke & Shi, Jianping & Fang, Hui, 2024. "Bifurcation and chaos analysis of a fractional-order delay financial risk system using dynamic system approach and persistent homology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 253-274.

    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. Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2022. "Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Liu, He & Dai, Chuanjun & Yu, Hengguo & Guo, Qing & Li, Jianbing & Hao, Aimin & Kikuchi, Jun & Zhao, Min, 2023. "Dynamics of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton and impulsive perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 368-386.
    3. Zheng, Yanlin & Gong, Xiang & Gao, Huiwang, 2022. "Selective grazing of zooplankton on phytoplankton defines rapid algal succession and blooms in oceans," Ecological Modelling, Elsevier, vol. 468(C).
    4. 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.
    5. Meng Zhu & Jing Li & Xinze Lian, 2022. "Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    6. Zhao, Qiuyue & Liu, Shutang & Niu, Xinglong, 2019. "Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 94-102.
    7. 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).
    8. Duan, Lian & Liu, Jinzhi & Huang, Chuangxia & Wang, Zengyun, 2022. "Finite-/fixed-time anti-synchronization of neural networks with leakage delays under discontinuous disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    9. 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.
    10. Li, Peiluan & Gao, Rong & Xu, Changjin & Ahmad, Shabir & Li, Ying & Akgül, Ali, 2023. "Bifurcation behavior and PDγ control mechanism of a fractional delayed genetic regulatory model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    11. 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.
    12. 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.
    13. 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.
    14. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Zhang, Minsong & Ding, Ling & Cao, Jinde & Alsaedi, Ahmed, 2020. "Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    15. Liao, Tiancai, 2024. "The impact of temperature variation on the algae–zooplankton dynamics with size-selective disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    16. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    17. Xiaomei Feng & Yuan Miao & Shulin Sun & Lei Wang, 2022. "Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    18. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2021. "Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 562-580.
    19. Muthaiah Subramanian & Jehad Alzabut & Mohamed I. Abbas & Chatthai Thaiprayoon & Weerawat Sudsutad, 2022. "Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and," Mathematics, MDPI, vol. 10(11), pages 1-19, May.
    20. 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.

    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:166:y:2023:i:c:s0960077922011547. 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.