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

Author

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  • 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
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    References listed on IDEAS

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    1. Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
    2. 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.
    3. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    4. 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.
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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    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).

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