IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v201y2025ip1s0960077925012470.html

Dynamical complexity in a discrete tri-trophic Rosenzweig–MacArthur system: Bifurcations, chaos and hybrid control

Author

Listed:
  • Goldar, Sujay

Abstract

We study the dynamical behavior of a discrete-time tri-trophic Rosenzweig–MacArthur predator–prey model with a superpredator. The continuous-time model is discretized using piecewise constant arguments to reflect non-overlapping generations and abrupt ecological interactions. We analyze the existence and stability of equilibria and derive conditions for local asymptotic stability and bifurcations, including transcritical, Neimark–Sacker, and period-doubling types, using Jury criterion and characteristic polynomial techniques. Numerical simulations demonstrate rich dynamics ranging from stable equilibria to high-period oscillations and chaos, showing that the discrete-time system exhibits greater complexity than its continuous counterpart. A hybrid control strategy that combines state feedback with parameter perturbation is proposed to suppress chaos while preserving ecological realism. The findings highlight the role of superpredators in shaping ecosystem stability and provide insights relevant to ecological forecasting, conservation, and pest management.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012470
    DOI: 10.1016/j.chaos.2025.117234
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925012470
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117234?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. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    2. Stephen Lynch, 2007. "Dynamical Systems with Applications using Mathematica®," Springer Books, Springer, number 978-0-8176-4586-1, January.
    3. 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).
    4. 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.
    5. Ghosh, Joydev & Sahoo, Banshidhar & Poria, Swarup, 2017. "Prey-predator dynamics with prey refuge providing additional food to predator," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 110-119.
    6. Qamar Din & A. A. Elsadany & Hammad Khalil, 2017. "Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-15, April.
    7. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
    8. Amer Tabakovic, 2015. "On the Characterization of Steady-States in Three-Dimensional Discrete Dynamical Systems," DEM Discussion Paper Series 15-16, Department of Economics at the University of Luxembourg.
    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. 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).
    2. Faisal Alsharif & Rizwan Ahmed & Ibrahim Alraddadi & Mohammed Alsubhi & Muhammad Amer & Md. Jasim Uddin, 2025. "A Study of Stability and Bifurcation in a Discretized Predator–Prey Model With Holling Type III Response and Prey Refuge Via Piecewise Constant Argument Method," Complexity, John Wiley & Sons, vol. 2025(1).
    3. 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.
    4. 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).
    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. 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.
    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. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.
    9. 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.
    10. Khalil Salem Nemer Al-Basyouni & Abdul Qadeer Khan, 2023. "Bifurcation Analysis of a Discrete‐Time Chemostat Model," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    11. Singh, Satyabhan & Gupta, Prajjwal & Priyadarshi, Anupam, 2026. "Unveiling multistability and chaos in a discretized predator–prey model incorporating harvesting and refuge: A study of Arnold tongues and shrimp-shaped periodic structures," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    12. Wang, Jinliang & Li, You & Zhong, Shihong & Hou, Xiaojie, 2019. "Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 1-17.
    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. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
    15. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    16. Luo, Tianjiao, 2019. "Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 396-410.
    17. Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.
    18. Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.
    19. Ojha, Archana & Mandal, Sayan & Singh, Ravikant & Thakur, Nilesh Kumar & Tiwari, Pankaj Kumar, 2025. "Predator–prey dynamics in autonomous and nonautonomous settings: Impacts of anti-predator behavior, refuge, and additional food," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    20. Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Bifurcation control of the Hodgkin–Huxley equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 217-224.

    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:201:y:2025:i:p1:s0960077925012470. 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.