IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2025y2025i1n5535248.html

Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys

Author

Listed:
  • Hersh Aziz Mohammed
  • Arkan Nawzad Mustafa

Abstract

In an ecological point of view, fears from predator cause physiological changes of prey population and these physiological changes may reduce the reproduction of prey. This paper deals with studying the effect of fear that is incorporated in the growth rate of prey on the dynamics of a delay ecological model consisting of two logistically growing prey species, namely, preyXand preyY, and a predator species. The predators take energy and biomass on predating on prey X as well as prey Y with extended Holling Type II functional response. We conduct a thorough analytical examination of the system, demonstrating the positivity and boundedness of the solutions. Criteria for the persistence of the model are founded. Seven biologically possible steady states are determined, and the local dynamics around the steady states based on the parameters are also investigated. Next, we investigated the occurrence of Hopf bifurcation around the prey X– and Y–free steady state, by taking the value of the time delay as a bifurcation parameter. Finally, we perform extensive numerical simulations to support the evidence of our analytical results and reveal the occurrence of Hopf bifurcation within the proposed model.

Suggested Citation

  • Hersh Aziz Mohammed & Arkan Nawzad Mustafa, 2025. "Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:5535248
    DOI: 10.1155/jama/5535248
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/jama/5535248
    Download Restriction: no
    File URL: https://libkey.io/10.1155/jama/5535248?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
    ---><---

    References listed on IDEAS

    as
    1. Basaznew Belew & Dawit Melese & Qiankun Song, 2022. "Modeling and Analysis of Predator-Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-14, December.
    2. R. Lavanya & S. Vinoth & K. Sathiyanathan & Zeric Njitacke Tabekoueng & P. Hammachukiattikul & R. Vadivel & Kenan Yildirim, 2022. "Dynamical Behavior of a Delayed Holling Type-II Predator-Prey Model with Predator Cannibalism," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, September.
    3. R. Lavanya & S. Vinoth & K. Sathiyanathan & Zeric Njitacke Tabekoueng & P. Hammachukiattikul & R. Vadivel, 2022. "Dynamical Behavior of a Delayed Holling Type‐II Predator‐Prey Model with Predator Cannibalism," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    4. Basaznew Belew & Dawit Melese, 2022. "Modeling and Analysis of Predator‐Prey Model with Fear Effect in Prey and Hunting Cooperation among Predators and Harvesting," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    5. Seralan Vinoth & R. Vadivel & Nien-Tsu Hu & Chin-Sheng Chen & Nallappan Gunasekaran, 2023. "Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    6. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, October.
    7. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    8. Zainab Saeed Abbas & Raid Kamel Naji, 2022. "Modeling and Analysis of the Influence of Fear on a Harvested Food Web System," Mathematics, MDPI, vol. 10(18), pages 1-37, September.
    9. Junli Liu & Pan Lv & Bairu Liu & Tailei Zhang & Eulalia Martinez, 2021. "Dynamics of a Predator-Prey Model with Fear Effect and Time Delay," Complexity, Hindawi, vol. 2021, pages 1-16, April.
    10. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco‐Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    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. Sozan Fuad Aziz & Hanaa Jamal Ahmed & Saiwan Majeed Fatah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of an Eco‐Epidemiological Model Incorporating Fear Effect and Prey Harvesting," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    2. Hanaa Jamal Ahmed & Kawther Yusuf Abdulrahman & Karzan Abdulrahman Hamzah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of Two‐Prey‐One‐Predator Model," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).

    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. Hiba Abdullah Ibrahim & Raid Kamel Naji, 2023. "The Impact of Fear on a Harvested Prey–Predator System with Disease in a Prey," Mathematics, MDPI, vol. 11(13), pages 1-28, June.
    2. Rasha Ali Hamodi & Karrar Qahtan Al-Jubouri & Reem Mudar Hussien & Raid Kamel Naji, 2025. "The Dynamical Analysis of Food‐Web System With a Group Defense and Antipredator Property," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    3. Yang, Yafei & Zhao, Xin & Fan, Meng, 2026. "Modeling the impact of Allee effect, herd behavior and harvesting on kelp beds: A cross-diffusion-ODE dynamical approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 525-554.
    4. Raid Kamel Naji & Reem Mudar Hussien, 2016. "The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    5. Sozan Fuad Aziz & Hanaa Jamal Ahmed & Saiwan Majeed Fatah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of an Eco‐Epidemiological Model Incorporating Fear Effect and Prey Harvesting," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    6. Basaznew Belew, 2025. "Analyzing the Effect of Fear, and Refuge on Prey, Harvesting, and Hunting Cooperation Among Predators on Leslie–Gower Predator Prey Model," International Journal of Differential Equations, John Wiley & Sons, vol. 2025(1).
    7. Reem Mudar Hussien & Raid Kamel Naji, 2023. "The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    8. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.
    9. Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
    10. Xiaoran Wang & Huimei Liu & Wencai Zhao, 2024. "A Predator–Prey System with a Modified Leslie–Gower and Prey Stage Structure Scheme in Deterministic and Stochastic Environments," Mathematics, MDPI, vol. 12(15), pages 1-26, July.
    11. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    12. Debasis Mukherjee, 2025. "Dynamics of a Stochastic Predator-Prey System in Presence of Competitor for Prey with Fear Effect and Hunting Cooperation," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-15, June.
    13. Chen Zhang & Xianyi Li, 2023. "Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response," Mathematics, MDPI, vol. 11(15), pages 1-19, July.
    14. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    15. Liu, Yang & Tian, Yuan & Sun, Kaibiao, 2025. "Dynamic properties and fishing behavior analysis of a predator-prey model with carrying-over fear and Allee effects," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    16. Karmakar, Souvick & Mondal, Nirmalya & Samanta, Guruprasad & Perc, Matjaž, 2025. "Prey-predator dynamics with adaptive hawk-dove strategies," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    17. Saha, Sangeeta & Pal, Swadesh & Melnik, Roderick, 2025. "Analysis of the impact of fear in the presence of additional food and prey refuge with nonlocal predator–prey models," Ecological Modelling, Elsevier, vol. 505(C).
    18. Hanaa Jamal Ahmed & Kawther Yusuf Abdulrahman & Karzan Abdulrahman Hamzah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of Two‐Prey‐One‐Predator Model," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    19. Guo, Zhenghua & Liu, Junli & Li, Bohan & Zhang, Tailei, 2026. "Stability analysis of a delayed predator–prey model with generalist predator and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    20. Das, Meghadri & Samanta, G.P., 2020. "A delayed fractional order food chain model with fear effect and prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 218-245.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnljam:v:2025:y:2025:i:1:n:5535248. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.