IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v93y2016icp20-31.html
   My bibliography  Save this article

Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response

Author

Listed:
  • Salman, S.M.
  • Yousef, A.M.
  • Elsadany, A.A.

Abstract

A discrete predator-prey system with square root functional response is presented. We study the existence and local stability analysis of the system. The conditions of existence of flip and Niemark-Sacker bifurcations in the system are derived. Furthermore, the chaotic behavior of the system in the sense of Marotto is proved. Numerical simulations are performed to show the consistence with analytical results and also to exhibit the complexity of the system. Finally, chaos control in the system is achieved via OGY feedback control method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:93:y:2016:i:c:p:20-31
    DOI: 10.1016/j.chaos.2016.09.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916302727
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.09.020?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. Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
    2. 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.
    3. Paolo Russu, 2012. "Controlling Complex Dynamics in a Protected Area Discrete-Time Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, March.
    4. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    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. Jialin Chen & Xiaqing He & Fengde Chen, 2021. "The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    2. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. 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.
    5. Kumar, Sachin & Kharbanda, Harsha, 2019. "Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 19-28.
    6. 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).

    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. Sun, Huijing & Cao, Hongjun, 2007. "Bifurcations and chaos of a delayed ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1383-1393.
    2. 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).
    3. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Dohtani, Akitaka, 2011. "Chaos resulting from nonlinear relations between different variables," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 290-297.
    9. Li, Yan & Wang, Lidong, 2019. "Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 116-126.
    10. 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.
    11. 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.
    12. Ekaterina Ekaterinchuk & Jochen Jungeilges & Tatyana Ryazanova & Iryna Sushko, 2017. "Dynamics of a minimal consumer network with uni-directional influence," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 831-857, November.
    13. Gardini, Laura & Sushko, Iryna & Avrutin, Viktor & Schanz, Michael, 2011. "Critical homoclinic orbits lead to snap-back repellers," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 433-449.
    14. Zhao, Yi & Xie, Lingli & Yiu, K.F. Cedric, 2009. "An improvement on Marotto’s theorem and its applications to chaotification of switching systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2225-2232.
    15. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, September.
    16. Rahman, Aminur & Blackmore, Denis, 2017. "Threshold voltage dynamics of chaotic RS flip-Flops," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 555-566.
    17. Soukaina, Ben Rhila & Imane, Agmour & Mostafa, Rachik & Naceur, Achtaich & Youssef, El Foutayeni, 2022. "Optimal control of a phytoplankton-zooplankton spatiotemporal discrete bioeconomic model," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    18. Banda, Heather & Chapwanya, Michael & Dumani, Phindile, 2022. "Pattern formation in the Holling–Tanner predator–prey model with predator-taxis. A nonstandard finite difference approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 336-353.
    19. Simas, Fabiano C. & Nobrega, K.Z. & Bazeia, D., 2022. "Bifurcation and chaos in one dimensional chains of small particles," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. 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.

    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:93:y:2016:i:c:p:20-31. 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.