IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp414-438.html
   My bibliography  Save this article

Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases

Author

Listed:
  • Du, Wentong
  • Xiao, Min
  • Ding, Jie
  • Yao, Yi
  • Wang, Zhengxin
  • Yang, Xinsong

Abstract

In this paper, a delayed fractional-order predator–prey system with trans-species infectious diseases is proposed and the corresponding control strategy is implemented via fractional-order proportional-derivative (PD) control. Firstly, for the uncontrolled fractional-order predator–prey system, explicit conditions of stability and Hopf bifurcation are established by selecting time delay as the bifurcation parameter. The predator–prey system will lose its stability and a family of oscillations will emerge when the time delay passes through the critical value. Secondly, under the fractional-order PD control, the influences of the controller on the system stability and bifurcation are investigated. It is demonstrated that the Hopf bifurcation can be postponed or advanced, and the desired dynamic can be achieved by choosing appropriate control gain parameters. In addition, the impacts of fractional order and control parameters on dynamics are explored. Finally, some numerical simulations are depicted to validate the theoretical results.

Suggested Citation

  • Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:414-438
    DOI: 10.1016/j.matcom.2022.10.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004153
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.10.014?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. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 293-310.
    2. Jin, Ting & Yang, Xiangfeng, 2021. "Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 203-221.
    3. 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.
    4. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    5. Hao, Pengmiao & Wang, Xuechen & Wei, Junjie, 2018. "Hopf bifurcation analysis of a diffusive single species model with stage structure and strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 153(C), pages 1-14.
    6. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. Zhao, LiuWei & Du, Jianguo & Wang, QiWei, 2019. "Nonlinear analysis and chaos control of the complex dynamics of multi-market Cournot game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 45-57.
    8. Peng, Yahong & Zhang, Guoying, 2020. "Dynamics analysis of a predator–prey model with herd behavior and nonlocal prey competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 366-378.
    9. Wang, Xuedi & Peng, Miao & Liu, Xiuyu, 2015. "Stability and Hopf bifurcation analysis of a ratio-dependent predator–prey model with two time delays and Holling type III functional response," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 496-508.
    10. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    11. Xu, Changjin & Liu, Zixin & Liao, Maoxin & Li, Peiluan & Xiao, Qimei & Yuan, Shuai, 2021. "Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 471-494.
    12. Hajimolana, S. Ahmad & Hussain, M. Azlan & Daud, W.M. Ashri Wan & Soroush, M. & Shamiri, A., 2011. "Mathematical modeling of solid oxide fuel cells: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(4), pages 1893-1917, May.
    13. Hu, Guang-Ping & Li, Wan-Tong & Yan, Xiang-Ping, 2009. "Hopf bifurcations in a predator–prey system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1273-1285.
    14. Hanif, Hanifa, 2022. "A computational approach for boundary layer flow and heat transfer of fractional Maxwell fluid," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 1-13.
    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. 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).
    2. Liang Cao & Azhar Halik & Ahmadjan Muhammadhaji, 2023. "Further Studies on the Dynamics of a Lotka–Volterra Competitor–Competitor–Mutualist System with Time-Varying Delays," Mathematics, MDPI, vol. 11(13), pages 1-14, June.

    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. Peng, Miao & Zhang, Zhengdi & Qu, Zifang & Bi, Qinsheng, 2020. "Qualitative analysis in a delayed Van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    2. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    3. Li, Ning & Yan, Mengting, 2022. "Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    4. Chen, Xiaoxiao & Wang, Xuedi, 2019. "Qualitative analysis and control for predator-prey delays system," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 361-372.
    5. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    6. 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.
    7. Sorce, A. & Greco, A. & Magistri, L. & Costamagna, P., 2014. "FDI oriented modeling of an experimental SOFC system, model validation and simulation of faulty states," Applied Energy, Elsevier, vol. 136(C), pages 894-908.
    8. Tera, Ibrahim & Zhang, Shengan & Liu, Guilian, 2024. "A conceptual hydrogen, heat and power polygeneration system based on biomass gasification, SOFC and waste heat recovery units: Energy, exergy, economic and emergy (4E) assessment," Energy, Elsevier, vol. 295(C).
    9. Xu, Yuan-wu & Wu, Xiao-long & Zhong, Xiao-bo & Zhao, Dong-qi & Sorrentino, Marco & Jiang, Jianhua & Jiang, Chang & Fu, Xiaowei & Li, Xi, 2021. "Mechanism model-based and data-driven approach for the diagnosis of solid oxide fuel cell stack leakage," Applied Energy, Elsevier, vol. 286(C).
    10. Pan, Zeyu & Gao, Yin & Yuan, Lin, 2021. "Bermudan options pricing formulas in uncertain financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. He, Zhongjie & Birgersson, E. & Li, Hua, 2014. "Reduced non-isothermal model for the planar solid oxide fuel cell and stack," Energy, Elsevier, vol. 70(C), pages 478-492.
    12. Maciej Ławryńczuk, 2018. "Towards Reduced-Order Models of Solid Oxide Fuel Cell," Complexity, Hindawi, vol. 2018, pages 1-18, July.
    13. Calise, Francesco & Cappiello, Francesco Liberato & Cimmino, Luca & Dentice d’Accadia, Massimo & Vicidomini, Maria, 2023. "Renewable smart energy network: A thermoeconomic comparison between conventional lithium-ion batteries and reversible solid oxide fuel cells," Renewable Energy, Elsevier, vol. 214(C), pages 74-95.
    14. Bilazeroğlu, Ş. & Göktepe, S. & Merdan, H., 2023. "Effects of the random walk and the maturation period in a diffusive predator–prey system with two discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    15. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    16. Paola Costamagna & Simone Grosso & Rowland Travis & Loredana Magistri, 2015. "Integrated Planar Solid Oxide Fuel Cell: Steady-State Model of a Bundle and Validation through Single Tube Experimental Data," Energies, MDPI, vol. 8(11), pages 1-24, November.
    17. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    18. Zarabi Golkhatmi, Sanaz & Asghar, Muhammad Imran & Lund, Peter D., 2022. "A review on solid oxide fuel cell durability: Latest progress, mechanisms, and study tools," Renewable and Sustainable Energy Reviews, Elsevier, vol. 161(C).
    19. Xiang Wang & Chang-Franw Lee & Jiabei Jiang & Xiaoyang Zhu, 2023. "Discussion on Sustainable Development Strategy of China’s Rehabilitation Assistive Device Industry Based on Diamond Model," Sustainability, MDPI, vol. 15(3), pages 1-24, January.
    20. Rhushikesh Ghotkar & Ryan J. Milcarek, 2022. "Modeling of the Kinetic Factors in Flame-Assisted Fuel Cells," Sustainability, MDPI, vol. 14(7), pages 1-18, March.

    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:matcom:v:205:y:2023:i:c:p:414-438. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.