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Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

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  • P. K. Santra
  • G. S. Mahapatra
  • G. R. Phaijoo

Abstract

The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

Suggested Citation

  • P. K. Santra & G. S. Mahapatra & G. R. Phaijoo, 2020. "Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-18, January.
    • Handle: RePEc:hin:jnlmpe:5309814
    DOI: 10.1155/2020/5309814
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    Cited by:

    1. Mondal, Chirodeep & Kesh, Dipak & Mukherjee, Debasis, 2023. "Global stability and bifurcation analysis of an infochemical induced three species discrete-time phytoplankton–zooplankton model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. 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.

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