IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2020y2020i1n5373817.html

Order and Chaos in a Prey‐Predator Model Incorporating Refuge, Disease, and Harvesting

Author

Listed:
  • Dahlia Khaled Bahlool
  • Huda Abdul Satar
  • Hiba Abdullah Ibrahim

Abstract

In this paper, a mathematical model consisting of a prey‐predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type‐II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

Suggested Citation

  • Dahlia Khaled Bahlool & Huda Abdul Satar & Hiba Abdullah Ibrahim, 2020. "Order and Chaos in a Prey‐Predator Model Incorporating Refuge, Disease, and Harvesting," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:5373817
    DOI: 10.1155/2020/5373817
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2020/5373817
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/5373817?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. 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.
    2. Naji, R.K. & Balasim, A.T., 2007. "On the dynamical behavior of three species food web model," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1636-1648.
    3. Naji, Raid Kamel & Balasim, Alla Tariq, 2007. "Dynamical behavior of a three species food chain model with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1853-1866.
    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. Rasha A. Ali & Hiba Abdullah Ibrahim, 2025. "Role of Wind and Fear on the Dynamic of a Prey and Two Competing Predators," Journal of Applied Mathematics, 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. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    2. Florencia Carusela, M. & Momo, Fernando R. & Romanelli, Lilia, 2009. "Competition, predation and coexistence in a three trophic system," Ecological Modelling, Elsevier, vol. 220(19), pages 2349-2352.
    3. 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.
    4. Cai, Liming & Li, Xuezhi & Yu, Jingyuan & Zhu, Guangtian, 2009. "Dynamics of a nonautonomous predator–prey dispersion–delay system with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2064-2075.
    5. Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.
    6. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Qi, Haokun & Liu, Bing & Li, Shi, 2024. "Stability, bifurcation, and chaos of a stage-structured predator-prey model under fear-induced and delay," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    8. 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.
    9. Gupta, R.P. & Yadav, Dinesh K., 2023. "Nonlinear dynamics of a stage-structured interacting population model with honest signals and cues," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    10. Hunki Baek & Dongseok Kim, 2014. "Dynamics of a Predator‐Prey System with Mixed Functional Responses," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    11. 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.
    12. Paul, Biswajit & Sikdar, Gopal Chandra & Ghosh, Uttam, 2025. "Effect of fear and non-linear predator harvesting on a predator–prey system in presence of environmental variability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 442-460.
    13. 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).
    14. 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.
    15. 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.
    16. 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).
    17. Karmakar, Souvick & Mondal, Nirmalya & Samanta, Guruprasad & Perc, Matjaž, 2025. "Prey-predator dynamics with adaptive hawk-dove strategies," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    18. 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).
    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. Ivanov, Tihomir & Dimitrova, Neli, 2017. "A predator–prey model with generic birth and death rates for the predator and Beddington–DeAngelis functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 111-123.

    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:2020:y:2020:i:1:n:5373817. 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.