IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v226y2024icp474-499.html

Dynamic analysis of a fast slow modified Leslie–Gower predator–prey model with constant harvest and stochastic factor

Author

Listed:
  • Li, Zhenlei
  • Zhang, Yue

Abstract

In this paper, the dynamic properties of a fast slow modified Leslie–Gower predator–prey model with constant harvest are discussed. The results show that the system appears different Hopf bifurcations and limit cycles as parameters change, and the stability of the internal equilibriums changes accordingly. The system also appears Bogdanov–Takens bifurcation phenomenon. For the fast–slow system of this model, the second order approximate perturbation manifolds, and an approximate manifold passing the fold point are constructed. Then using the criterion of inflection point curve and blow-up method, the existence of canard cycles is analyzed. By comparing with the model with nonlinear harvest, the different effects of constant harvest on the model are highlighted. In addition, the effect of stochastic factors on the fast–slow system is considered.

Suggested Citation

  • Li, Zhenlei & Zhang, Yue, 2024. "Dynamic analysis of a fast slow modified Leslie–Gower predator–prey model with constant harvest and stochastic factor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 474-499.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:474-499
    DOI: 10.1016/j.matcom.2024.07.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424002842
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.07.027?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. Zhao, Dianli & Yuan, Sanling, 2016. "Dynamics of the stochastic Leslie–Gower predator–prey system with randomized intrinsic growth rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 419-428.
    2. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
    3. Shang, Zuchong & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2021. "Bifurcation analysis in a predator–prey system with an increasing functional response and constant-yield prey harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 976-1002.
    4. Umrao, Anuj Kumar & Roy, Subarna & Tiwari, Pankaj Kumar & Srivastava, Prashant K., 2024. "Dynamical behaviors of autonomous and nonautonomous models of generalist predator–prey system with fear, mutual interference and nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    5. Yufeng Wang & Youhua Qian & Bingwen Lin, 2020. "Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models," Complexity, Hindawi, vol. 2020, pages 1-11, September.
    6. Xin Ai & Xinyu Liu & Yuting Ding & Han Li, 2022. "Dynamic Analysis of a COVID-19 Vaccination Model with a Positive Feedback Mechanism and Time-Delay," Mathematics, MDPI, vol. 10(9), pages 1-24, May.
    7. Xu, Dongsheng & Liu, Ming & Xu, Xiaofeng, 2020. "Analysis of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    8. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    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. Ai, Xin & Zhang, Yue, 2025. "Dynamic analysis of phytoplankton–zooplankton–fish singular perturbation system on three time-scales," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    2. Qi, Haokun & Jin, Jiani & Liu, Bing, 2026. "Basic reproduction number of a deterministic and stochastic predator–prey model with novel fear functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 476-497.
    3. Min, Feng & Xiao, Min & Cao, Jinde & Wang, Zhen & Ding, Jie & Rutkowski, Leszek, 2025. "Spatiotemporal dynamics of a food chain model incorporating higher-order interactions and slow–fast effect," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).

    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. Yao, Yong, 2025. "Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 32-49.
    2. Shang, Zuchong & Qiao, Yuanhua, 2023. "Multiple bifurcations in a predator–prey system of modified Holling and Leslie type with double Allee effect and nonlinear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 745-764.
    3. Xiaoqing Wen & Yue Chen & Hongwei Yin, 2016. "Positive Solutions of a Diffusive Predator‐Prey System including Disease for Prey and Equipped with Dirichlet Boundary Condition," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    4. Dai, Chuanyu & Wang, Qinglong & Liu, Zhijun & Yan, Qian, 2025. "Trade-off dynamics of predator–prey system incorporating variable carrying capacity and wind effect," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    5. Xue, Yalong & Chen, Shengjiang & Xu, Lili & Chen, Fengde, 2025. "Fear-driven gregariousness and survival: Modeling bidirectional feedbacks and seasonality in a generalist predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    7. Singh, Yovan & Ghosh, Bapan & Mondal, Suman, 2026. "Delay-induced multiple stability scenarios, species coexistence, and predator extinction in an ecological system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 243(C), pages 171-195.
    8. Xia Liu & Jinling Wang, 2013. "Bogdanov‐Takens and Triple Zero Bifurcations of a Delayed Modified Leslie‐Gower Predator Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. 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.
    10. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    11. Sarif, Nawaj & Kumar, Arjun & Anshu, & Sarwardi, Sahabuddin & Dubey, Balram, 2024. "Spatio-temporal dynamics in a delayed prey–predator model with nonlinear prey refuge and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    12. Jiao Jiang & Yongli Song, 2013. "Stability and Bifurcation Analysis of a Delayed Leslie‐Gower Predator‐Prey System with Nonmonotonic Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    13. Guodong Liu & Xiaohong Wang & Xinzhu Meng & Shujing Gao, 2017. "Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps," Complexity, Hindawi, vol. 2017, pages 1-15, June.
    14. Chen, Xingzhi & Tian, Baodan & Xu, Xin & Zhang, Hailan & Li, Dong, 2023. "A stochastic predator–prey system with modified LG-Holling type II functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 449-485.
    15. 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.
    16. Yin, Hongwei & Zhou, Jiaxing & Xiao, Xiaoyong & Wen, Xiaoqing, 2014. "Analysis of a diffusive Leslie–Gower predator–prey model with nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 51-61.
    17. Liu, Qun & Jiang, Daqing & He, Xiuli & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 273-287.
    18. Chen, Mengxin & Wu, Ranchao, 2023. "Steady states and spatiotemporal evolution of a diffusive predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    19. Huangyu Guo & Jing Han & Guodong Zhang, 2023. "Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    20. Yong Ye & Hua Liu & Yu-mei Wei & Ming Ma & Kai Zhang, 2019. "Dynamic Study of a Predator‐Prey Model with Weak Allee Effect and Delay," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(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:226:y:2024:i:c:p:474-499. 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.