IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i10p1702-d816544.html
   My bibliography  Save this article

Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator

Author

Listed:
  • Ajay Kumar

    (Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India)

  • Sara Salem Alzaid

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia)

  • Badr Saad T. Alkahtani

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia)

  • Sunil Kumar

    (Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India
    Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates
    Department of Mathematics, University Centre for Research and Development, Chandigarh University, Gharuan, Mohali 140413, Punjab, India)

Abstract

We apply a new generalized Caputo operator to investigate the dynamical behaviour of the non-integer food web model (FWM). This dynamical model has three population species and is nonlinear. Three types of species are considered in this population: prey species, intermediate predators, and top predators, and the top predators are also divided into mature and immature predators. We calculated the uniqueness and existence of the solutions applying the fixed-point hypothesis. Our study examines the possibility of obtaining new dynamical phase portraits with the new generalized Caputo operator and demonstrates the portraits for several values of fractional order. A generalized predictor–corrector (P-C) approach is utilized in numerically solving this food web model. In the case of the nonlinear equations system, the effectiveness of the used scheme is highly evident and easy to implement. In addition, stability analysis was conducted for this numerical scheme.

Suggested Citation

  • Ajay Kumar & Sara Salem Alzaid & Badr Saad T. Alkahtani & Sunil Kumar, 2022. "Complex Dynamic Behaviour of Food Web Model with Generalized Fractional Operator," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1702-:d:816544
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/10/1702/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/10/1702/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kumar, Ajay & Kumar, Sunil, 2022. "A study on eco-epidemiological model with fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Khan, Aziz & Abdeljawad, Thabet & Gómez-Aguilar, J.F. & Khan, Hasib, 2020. "Dynamical study of fractional order mutualism parasitism food web module," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Erturk, Vedat Suat & Kumar, Pushpendra, 2020. "Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 139(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. A. E. Matouk & T. N. Abdelhameed & D. K. Almutairi & M. A. Abdelkawy & M. A. E. Herzallah, 2023. "Existence of Self-Excited and Hidden Attractors in the Modified Autonomous Van Der Pol-Duffing Systems," Mathematics, MDPI, vol. 11(3), pages 1-13, January.

    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. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Shloof, A.M. & Senu, N. & Ahmadian, A. & Salahshour, Soheil, 2021. "An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 415-435.
    5. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Ravichandran, C. & Sowbakiya, V. & Nisar, Kottakkaran Sooppy, 2022. "Study on existence and data dependence results for fractional order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Kumar, Ajay & Kumar, Sunil, 2022. "A study on eco-epidemiological model with fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Begum, Razia & Tunç, Osman & Khan, Hasib & Gulzar, Haseena & Khan, Aziz, 2021. "A fractional order Zika virus model with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    10. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    11. Luo, Ziyang & Zhang, Xingdong & Wang, Shuo & Yao, Lin, 2022. "Numerical approximation of time fractional partial integro-differential equation based on compact finite difference scheme," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    12. Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    13. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    14. Singh, Harendra & Baleanu, Dumitru & Singh, Jagdev & Dutta, Hemen, 2021. "Computational study of fractional order smoking model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    15. Liao, Xiaozhong & Ran, Manjie & Yu, Donghui & Lin, Da & Yang, Ruocen, 2022. "Chaos analysis of Buck converter with non-singular fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    16. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    17. Das, Parthasakha & Das, Samhita & Das, Pritha & Rihan, Fathalla A. & Uzuntarla, Muhammet & Ghosh, Dibakar, 2021. "Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    18. Matouk, A.E. & Lahcene, Bachioua, 2023. "Chaotic dynamics in some fractional predator–prey models via a new Caputo operator based on the generalised Gamma function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    19. Li, Xiaoyan, 2021. "Comment for “Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel”," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    20. Mashayekhi, S. & Sedaghat, S., 2021. "Fractional model of stem cell population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

    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:10:y:2022:i:10:p:1702-:d:816544. 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.