IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v252y2015icp324-335.html
   My bibliography  Save this article

Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey

Author

Listed:
  • Dhar, Joydip
  • Singh, Harkaran
  • Bhatti, Harbax Singh

Abstract

In the present study, the stability and bifurcation analysis of discrete-time predator–prey system with predator partially dependent on prey and crowding effect of predator is examined. Global stability of the system at the fixed points has been discussed. The specific conditions for existence of flip bifurcation and Hopf bifurcation in the interior of R+2 have been derived by using a center manifold theorem and bifurcation theory. Numerical simulations have been carried out to show the complex dynamical behavior of the system and to justify our analytic results. In case of flip bifurcation, numerical simulations presented cascade of period-doubling bifurcation in the orbits of period 2, 4, 8, chaotic orbits and stable window of period 9 orbit; whereas in case of Hopf bifurcation, smooth invariant circle bifurcates from the fixed point. The complexity of dynamical behavior is confirmed by computation of Lyapunov exponents.

Suggested Citation

  • Dhar, Joydip & Singh, Harkaran & Bhatti, Harbax Singh, 2015. "Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 324-335.
  • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:324-335
    DOI: 10.1016/j.amc.2014.12.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314016750
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2014.12.021?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. Sun, Gui-Quan & Jin, Zhen & Liu, Quan-Xing & Li, Li, 2008. "Dynamical complexity of a spatial predator–prey model with migration," Ecological Modelling, Elsevier, vol. 219(1), pages 248-255.
    2. Chen, Yuanyuan & Changming, Song, 2008. "Stability and Hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1104-1114.
    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. Xiongxiong Du & Xiaoling Han & Ceyu Lei, 2022. "Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    2. Zhang, Limin & Zhang, Chaofeng & He, Zhirong, 2019. "Codimension-one and codimension-two bifurcations of a discrete predator–prey system with strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 155-178.
    3. Abbasi, Muhammad Aqib & Samreen, Maria, 2024. "Analyzing multi-parameter bifurcation on a prey–predator model with the Allee effect and fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

    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. Xiongxiong Du & Xiaoling Han & Ceyu Lei, 2022. "Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    2. Zeyan Wu & Wenxiong Lin & Bailian Li & Linkun Wu & Changxun Fang & Zhixing Zhang, 2015. "Terminal Restriction Fragment Length Polymorphism Analysis of Soil Bacterial Communities under Different Vegetation Types in Subtropical Area," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-10, June.
    3. Ling, Li & Wang, Weiming, 2009. "Dynamics of a Ivlev-type predator–prey system with constant rate harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2139-2153.
    4. Xibo Wang & Jianping Ge & Wendong Wei & Hanshi Li & Chen Wu & Ge Zhu, 2016. "Spatial Dynamics of the Communities and the Role of Major Countries in the International Rare Earths Trade: A Complex Network Analysis," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-22, May.
    5. Wang, Caiyun, 2015. "Rich dynamics of a predator–prey model with spatial motion," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 1-9.
    6. 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.
    7. 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).
    8. Tousheng Huang & Huayong Zhang & Xuebing Cong & Ge Pan & Xiumin Zhang & Zhao Liu, 2019. "Exploring Spatiotemporal Complexity of a Predator-Prey System with Migration and Diffusion by a Three-Chain Coupled Map Lattice," Complexity, Hindawi, vol. 2019, pages 1-19, May.
    9. Fasani, Stefano & Rinaldi, Sergio, 2011. "Factors promoting or inhibiting Turing instability in spatially extended prey–predator systems," Ecological Modelling, Elsevier, vol. 222(18), pages 3449-3452.
    10. Chang, Lili & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen, 2015. "Rich dynamics in a spatial predator–prey model with delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 540-550.
    11. 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.
    12. Wu, Xingjie & Huang, Wentao, 2009. "Dynamic analysis of a one-prey multi-predator impulsive system with Ivlev-type functional," Ecological Modelling, Elsevier, vol. 220(6), pages 774-783.

    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:apmaco:v:252:y:2015:i:c:p:324-335. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.