IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v243y2026icp149-170.html

Nonlinear dynamics and Chaos control in a discrete predator–prey model with Smith-type growth, cannibalism, and group defense

Author

Listed:
  • Khan, Md. Mutakabbir

Abstract

This work investigates the nonlinear dynamics of a discrete predator–prey system with prey cannibalism and group defense. The model combines Smith-type growth with a cannibalistic term for prey, while predators follow a Monod–Haldane response. Using the center manifold theorem, we establish conditions for period-doubling (PD) and Neimark–Sacker (NS) bifurcations within the biologically feasible region. Numerical simulations validate these theoretical results and reveal complex dynamics, including high-periodic orbits, quasi-periodic invariant closed curves, and chaotic attractors confirmed through maximal Lyapunov exponents. To suppress chaotic fluctuations and restore ecological balance, we implement both the Ott–Grebogi–Yorke (OGY) method and a state feedback control strategy, successfully stabilizing the system near unstable equilibria. This work deepens the understanding of nonlinear mechanisms governing ecological interactions and offers robust control strategies to manage chaos in discrete biological systems.

Suggested Citation

  • Khan, Md. Mutakabbir, 2026. "Nonlinear dynamics and Chaos control in a discrete predator–prey model with Smith-type growth, cannibalism, and group defense," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 243(C), pages 149-170.
    • Handle: RePEc:eee:matcom:v:243:y:2026:i:c:p:149-170
    DOI: 10.1016/j.matcom.2025.11.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475425004938
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.11.028?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. Scott Creel & Paul Schuette & David Christianson, 2014. "Effects of predation risk on group size, vigilance, and foraging behavior in an African ungulate community," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(4), pages 773-784.
    2. Huo, Liang’an & Jiang, Jiehui & Gong, Sixing & He, Bing, 2016. "Dynamical behavior of a rumor transmission model with Holling-type II functional response in emergency event," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 228-240.
    3. Han, Xiaoling & Lei, Ceyu, 2023. "Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with Smith growth function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. 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).
    5. Stephen Lynch, 2007. "Dynamical Systems with Applications using Mathematica®," Springer Books, Springer, number 978-0-8176-4586-1, March.
    6. Feng, Xiaozhou & Liu, Xia & Sun, Cong & Jiang, Yaolin, 2023. "Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    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. 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).
    2. Li, Lu & Yan, Xiang-Ping & Zhang, Cun-Hua, 2025. "Turing, Hopf and Turing–Hopf bifurcations in a modified Leslie–Gower predator–prey diffusive system with Smith prey growth and nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    3. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    4. Jiang, Jiehui & Ma, Jie, 2023. "Dynamic analysis of pandemic cross-regional transmission considering quarantine strategies in the context of limited medical resources," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    5. Yang Zhao & Chun-Xiao Huang & Yiming Gu & Yacong Zhao & Wenjie Ren & Yutong Wang & Jinjin Chen & Na N. Guan & Jianren Song, 2024. "Serotonergic modulation of vigilance states in zebrafish and mice," Nature Communications, Nature, vol. 15(1), pages 1-18, December.
    6. 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).
    7. Li, Tianhua & Zhang, Xuetian & Zhang, Chunrui, 2024. "Pattern dynamics analysis of a space–time discrete spruce budworm model," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    8. Mu, Yu & Lo, Wing-Cheong & Tan, Yuanshun & Liu, Zijian, 2025. "Hybrid control for the prey in a spatial prey-predator model with cooperative hunting and fear effect time lag," Applied Mathematics and Computation, Elsevier, vol. 491(C).
    9. Ramasamy, Sivasamy & Banjerdpongchai, David & Park, PooGyeon, 2025. "Stability and Hopf-bifurcation analysis of diffusive Leslie–Gower prey–predator model with the Allee effect and carry-over effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 19-40.
    10. Zhang, Yuhuai & Zhu, Jianjun, 2018. "Stability analysis of I2S2R rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 862-881.
    11. Qiuyue Zhao & Xinglong Niu, 2024. "Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense," Mathematics, MDPI, vol. 12(12), pages 1-14, June.
    12. Jianli Xiao & Hanli Xiao & Xinchang Zhang, 2025. "Complex Dynamics in the Platform Ecosystem Competition Model Between IHAs and THAs," SAGE Open, , vol. 15(2), pages 21582440251, May.
    13. Salehi, Khayyam & Alidousti, Javad, 2026. "The dynamic behavior of time-delayed Leslie-Gower predator-prey model," Applied Mathematics and Computation, Elsevier, vol. 508(C).
    14. Menon, Sidharth & Kumari, Sangeeta, 2025. "Impact of cross-diffusion and Allee effect on modified Leslie–Gower model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 183-199.
    15. Singh, Piyush Pratap & Roy, Binoy Krishna, 2022. "Chaos and multistability behaviors in 4D dissipative cancer growth/decay model with unstable line of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    16. Kumbhakar, Ruma & Hossain, Mainul & Pal, Nikhil, 2024. "Dynamics of a two-prey one-predator model with fear and group defense: A study in parameter planes," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    17. Kumar, Vikas, 2024. "Pattern formation and delay-induced instability in a Leslie–Gower type prey–predator system with Smith growth function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 78-97.
    18. Wen, Mingyao & Zhang, Guang & Yan, Yubin, 2025. "Turing instability of a discrete competitive single diffusion-driven Lotka–Volterra model," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    19. Uddin, Md. Jasim & Naik, Parvaiz Ahmad & Eskandari, Zohreh & Monira, Sherajum & Huang, Zhengxin, 2026. "Complex dynamics and chaos control in a fractional-order discrete prey-predator model incorporating an Ivlev functional response and Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 300-325.
    20. 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).

    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:matcom:v:243:y:2026:i:c:p:149-170. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.