IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2025y2025i1n1566022.html

Stability Analysis of a Discrete‐Time Predator–Prey Model Using Piecewise Constant Argument

Author

Listed:
  • Muhammad Rafaqat
  • Abdou Al Zubaidi
  • Faisal Z. Duraihem
  • Jihad Younis
  • Syed Tauseef Saeed

Abstract

This paper offers a thorough analysis of the discrete‐time predator–prey model obtained by using the piecewise constant argument technique. Our principal findings demonstrate that the coexistence fixed exhibits rich dynamical behavior, undergoing both Neimark–Sacker and period‐doubling bifurcations as ecological parameters vary. These bifurcations lead to the emergence of quasiperiodic oscillations and chaotic dynamics, which pose significant threats to population persistence. To address this challenge, we develop a hybrid control strategy that effectively stabilizes the system by suppressing chaotic behavior and restoring predictable population dynamics. Numerical simulations confirm the efficacy of our control approach across different parameter regimes. The study provides ecologists with a practical methodology: employing bifurcation analysis to identify instability thresholds followed by targeted control intervention to maintain ecological stability, with particular relevance for managing vulnerable or harvested species.

Suggested Citation

  • Muhammad Rafaqat & Abdou Al Zubaidi & Faisal Z. Duraihem & Jihad Younis & Syed Tauseef Saeed, 2025. "Stability Analysis of a Discrete‐Time Predator–Prey Model Using Piecewise Constant Argument," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnddns:v:2025:y:2025:i:1:n:1566022
    DOI: 10.1155/ddns/1566022
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/ddns/1566022
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ddns/1566022?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. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
    Full references (including those not matched with items on IDEAS)

    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. Zhong, Shihong & Xia, Juandi & Liu, Biao, 2021. "Spatiotemporal dynamics analysis of a semi-discrete reaction-diffusion Mussel-Algae system with advection," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Mohammed O. Al-Kaff & Ghada AlNemer & Hamdy A. El-Metwally & Abd-Elalim A. Elsadany & Elmetwally M. Elabbasy, 2024. "Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model," Mathematics, MDPI, vol. 12(9), pages 1-20, April.
    3. Shuo Liang & Wenlong Wang & Chunrui Zhang, 2024. "Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices," Mathematics, MDPI, vol. 13(1), pages 1-45, December.
    4. Yousef, A.M. & Rida, S.Z. & Ali, H.M. & Zaki, A.S., 2023. "Stability, co-dimension two bifurcations and chaos control of a host-parasitoid model with mutual interference," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Xiaorong Ma & Qamar Din & Muhammad Rafaqat & Nasir Javaid & Yongliang Feng, 2020. "A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control," Mathematics, MDPI, vol. 8(4), pages 1-26, April.
    6. Bozkurt, Fatma & Yousef, Ali & Baleanu, Dumitru & Alzabut, Jehad, 2020. "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. S. Vinoth & R. Sivasamy & K. Sathiyanathan & B. Unyong & R. Vadivel & Nallappan Gunasekaran, 2022. "A Novel Discrete‐Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population," Complexity, John Wiley & Sons, vol. 2022(1).
    8. 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.
    9. Goldar, Sujay, 2025. "Dynamical complexity in a discrete tri-trophic Rosenzweig–MacArthur system: Bifurcations, chaos and hybrid control," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    10. Zhang, Huimin & Gao, Jian & Gu, Changgui & Long, Yongshang & Shen, Chuansheng & Yang, Huijie, 2024. "Turing-like patterns induced by the competition between two stable states in a discrete-time predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    11. Cui, Qianqian & Zhang, Qiang & Qiu, Zhipeng & Hu, Zengyun, 2016. "Complex dynamics of a discrete-time predator-prey system with Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 158-171.
    12. Bozkurt, Fatma & Yousef, Ali & Abdeljawad, Thabet & Kalinli, Adem & Mdallal, Qasem Al, 2021. "A fractional-order model of COVID-19 considering the fear effect of the media and social networks on the community," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    13. Sarker Md. Sohel Rana & Md. Jasim Uddin, 2023. "Dynamics and Control of a Discrete Predator–Prey Model with Prey Refuge: Holling Type I Functional Response," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    14. Xiao, Yanni & Tang, Sanyi, 2008. "The effect of initial density and parasitoid intergenerational survival rate on classical biological control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1048-1058.
    15. Changcheng Xiang & Yi Yang & Zhongyi Xiang & Wenjie Qin, 2016. "Numerical Analysis of Discrete Switching Prey‐Predator Model for Integrated Pest Management," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    16. Binhao Hong & Chunrui Zhang, 2023. "Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    17. Abdul Qadeer Khan & Ibraheem M. Alsulami & Umbreen Sadiq, 2022. "Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System," Complexity, John Wiley & Sons, vol. 2022(1).
    18. Akhtar, S. & Ahmed, R. & Batool, M. & Shah, Nehad Ali & Chung, Jae Dong, 2021. "Stability, bifurcation and chaos control of a discretized Leslie prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    19. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    20. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.

    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:jnddns:v:2025:y:2025:i:1:n:1566022. 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/3059 .

    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.