IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v120y2019icp158-170.html
   My bibliography  Save this article

Bifurcations and simulations of two predator–prey models with nonlinear harvesting

Author

Listed:
  • Lv, Yunfei
  • Pei, Yongzhen
  • Wang, Yong

Abstract

We propose and investigate a predator-prey model with selective nonlinear harvesting for the prey and predator, such harvesting increases smoothly to a limit value when the density of harvested population is large enough. The existence of nonlinear harvesting makes the dynamics of the model more complicated, including multiple equilibria, limit cycle, heteroclinic and homoclinic orbit, bistability, saddle-node bifurcation, transcritical bifurcation, subcritical and supercritical Hopf bifurcation and Bogdanov–Takens bifurcation. Furthermore, some numerical simulations are given to illustrate these results.

Suggested Citation

  • Lv, Yunfei & Pei, Yongzhen & Wang, Yong, 2019. "Bifurcations and simulations of two predator–prey models with nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 158-170.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:158-170
    DOI: 10.1016/j.chaos.2018.12.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919300311
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.12.038?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.
    2. Hu, Jiang-Hong & Xue, Ya-Kui & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2016. "Global dynamics of a predator–prey system modeling by metaphysiological approach," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 369-384.
    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. Li, Wenjie & Guan, Yajuan & Cao, Jinde & Xu, Fei, 2024. "Global dynamics and threshold control of a discontinuous fishery ecological system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Li, Xinxin & Yu, Hengguo & Dai, Chuanjun & Ma, Zengling & Wang, Qi & Zhao, Min, 2021. "Bifurcation analysis of a new aquatic ecological model with aggregation effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 75-96.
    3. Marick, Sounov & Bhattacharya, Santanu & Bairagi, Nandadulal, 2023. "Dynamic properties of a reaction–diffusion predator–prey model with nonlinear harvesting: A linear and weakly nonlinear analysis," Chaos, Solitons & Fractals, Elsevier, vol. 175(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. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Datta, Jyotiska & Jana, Debaldev & Upadhyay, Ranjit Kumar, 2019. "Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 229-235.
    3. 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).
    4. Wen, Haijun & Hou, Shiwang & Liu, Zhaohua & Liu, Yongjiang, 2017. "An optimization algorithm for integrated remanufacturing production planning and scheduling system," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 69-76.
    5. Wu, Zeyan & Li, Jianjuan & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2019. "A spatial predator–prey system with non-renewable resources," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 381-391.
    6. Yang, Ruizhi & Ma, Jian, 2018. "Analysis of a diffusive predator-prey system with anti-predator behaviour and maturation delay," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 128-139.
    7. Pal, D. & Samanta, G.P. & Mahapatra, G.S., 2017. "Selective harvesting of two competing fish species in the presence of toxicity with time delay," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 74-93.
    8. Li, Li, 2017. "Transmission dynamics of Ebola virus disease with human mobility in Sierra Leone," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 575-579.
    9. Wang, Jingjing & Zheng, Hongchan & Jia, Yunfeng, 2021. "Dynamical analysis on a bacteria-phages model with delay and diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    10. Liu, Chanjuan & Zhu, Enqiang, 2017. "Computational ability in games: Individual difference and dynamics," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 313-320.
    11. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar & Samanta, G.P., 2016. "Ecological dynamics of age selective harvesting of fish population: Maximum sustainable yield and its control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 111-122.
    12. Wang, Caiyun & Qi, Suying, 2018. "Spatial dynamics of a predator-prey system with cross diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 55-60.
    13. Wu, Zeyan & Li, Jianjuan & Li, Jing & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2017. "Pattern formations of an epidemic model with Allee effect and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 599-606.
    14. Zhang, Hong-Tao & Li, Li, 2018. "Traveling wave fronts of a single species model with cannibalism and nonlocal effect," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 148-153.
    15. Devi, Sapna & Gupta, Nivedita, 2019. "Effects of inclusion of delay in the imposition of environmental tax on the emission of greenhouse gases," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 41-53.
    16. N. S. N. V. K. Vyshnavi Devi & Debaldev Jana & M. Lakshmanan, 2020. "Interplay Between Reproduction and Age Selective Harvesting Delays of a Single Population Non-Autonomous System," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1857-1891, December.

    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:120:y:2019:i:c:p:158-170. 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: 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.