IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v200y2025ip2s0960077925010847.html

Dynamical transitions and chaos control in a discrete predator–prey model with Gompertz growth and Holling type III response

Author

Listed:
  • Almatrafi, M.B.
  • Berkal, Messaoud
  • Ahmed, Rizwan

Abstract

This study investigates the dynamics of a discrete predator–prey model derived from a continuous system using the forward Euler method. The model features Gompertz growth for the prey and a Holling type III functional response for the predator. We analyze the existence and local stability of equilibria and identify conditions under which the system exhibits period-doubling and Neimark–Sacker bifurcations, marking the onset of oscillatory and complex dynamics. To detect chaos, we apply the 0−1 chaos test, confirming irregular behavior in specific parameter regimes. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, phase portraits, and time series plots, demonstrate the model’s rich dynamical behavior. Two control strategies, hybrid control and state feedback control, are implemented to control bifurcation and chaos. Our findings highlight how nonlinear responses and discrete-time dynamics can generate unpredictable population patterns and provide tools for stabilizing ecological systems.

Suggested Citation

  • Almatrafi, M.B. & Berkal, Messaoud & Ahmed, Rizwan, 2025. "Dynamical transitions and chaos control in a discrete predator–prey model with Gompertz growth and Holling type III response," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010847
    DOI: 10.1016/j.chaos.2025.117071
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925010847
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117071?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Pati, N.C. & Layek, G.C. & Pal, Nikhil, 2020. "Bifurcations and organized structures in a predator-prey model with hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Arancibia-Ibarra, Claudio & Aguirre, Pablo & Flores, José & van Heijster, Peter, 2021. "Bifurcation analysis of a predator-prey model with predator intraspecific interactions and ratio-dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    3. G.C. Layek, 2015. "An Introduction to Dynamical Systems and Chaos," Springer Books, Springer, number 978-81-322-2556-0, October.
    4. Rizwan Ahmed & Muhammad Rafaqat & Imran Siddique & Mohammad Asif Arefin & A. E. Matouk, 2023. "Complex Dynamics and Chaos Control of a Discrete-Time Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-20, July.
    5. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    6. Mokni, Karima & Ch-Chaoui, Mohamed & Mondal, Bapin & Ghosh, Uttam, 2024. "Rich dynamics of a discrete two dimensional predator–prey model using the NSFD scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 992-1018.
    7. 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).
    8. Aulisa, Eugenio & Jang, Sophia R.-J., 2014. "Continuous-time predator–prey systems with Allee effects in the prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 1-16.
    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. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.
    2. Barman, Dipesh & Kumar Upadhyay, Ranjit, 2026. "Impact of carryover and fear-induced delays on population dynamics: A cross-model stability and bifurcation investigation," Applied Mathematics and Computation, Elsevier, vol. 516(C).
    3. Baydemir, Pinar & Merdan, Huseyin, 2025. "Bifurcation analysis, chaos control, and FAST approach for the complex dynamics of a discrete-time predator–prey system with a weak Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    4. Rebelo, Paulo & Rosa, Silvério, 2025. "An optimal control problem for a predator–prey model with strong and weak preys," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    5. Leutcho, Gervais Dolvis & Gandubert, Gabriel & Woodward, Lyne & Blanchard, François, 2025. "Electric-field-biased control of irregular oscillations via multistability in a nonlinear terahertz meta-atom," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    6. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.
    7. Hu, Zengyun & Teng, Zhidong & Zhang, Tailei & Zhou, Qiming & Chen, Xi, 2017. "Globally asymptotically stable analysis in a discrete time eco-epidemiological system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 20-31.
    8. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Vishwakarma, Krishnanand & Sen, Moitri, 2021. "Role of Allee effect in prey and hunting cooperation in a generalist predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 622-640.
    10. Pandey, Soumik & Ghosh, Uttam & Das, Debashis & Chakraborty, Sarbani & Sarkar, Abhijit, 2024. "Rich dynamics of a delay-induced stage-structure prey–predator model with cooperative behaviour in both species and the impact of prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 49-76.
    11. Pradhan, Dickcha & Ali, Khalid K. & Karakoc, Seydi Battal Gazi & Saha, Asit, 2026. "New families of soliton solutions and dynamics of nonlinear traveling waves for the Whitham–Broer–Kaup equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 376-390.
    12. He, Haoming & Xiao, Min & Lu, Yunxiang & Wang, Zhen & Tao, Binbin, 2023. "Control of tipping in a small-world network model via a novel dynamic delayed feedback scheme," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    13. Pranali Roy Chowdhury & Sergei Petrovskii & Malay Banerjee, 2022. "Effect of Slow–Fast Time Scale on Transient Dynamics in a Realistic Prey-Predator System," Mathematics, MDPI, vol. 10(5), pages 1-12, February.
    14. Chou, Yen-hsi & Chow, Yunshyong & Hu, Xiaochuan & Jang, Sophia R.-J., 2021. "A Ricker–type predator–prey system with hunting cooperation in discrete time," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 570-586.
    15. 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).
    16. Mokni, Karima & Ali, Halima Ben & Ghosh, Bapan & Ch-Chaoui, Mohamed, 2025. "Nonlinear dynamics of a Darwinian Ricker system with strong Allee effect and immigration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 789-813.
    17. Guangye Chen & Zhidong Teng & Zengyun Hu, 2011. "Analysis of stability for a discrete ratio-dependent predator-prey system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(1), pages 1-26, February.
    18. 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).
    19. Liu, Chao & Lu, Na & Zhang, Qingling, 2017. "Dynamical analysis in a hybrid bioeconomic system with multiple time delays and strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 104-131.
    20. Yanfei Du & Ben Niu & Junjie Wei, 2021. "Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect," Mathematics, MDPI, vol. 9(24), pages 1-40, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:eee:chsofr:v:200:y:2025:i:p2:s0960077925010847. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.