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Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response

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  • S. M. Sohel Rana
  • Umme Kulsum

Abstract

The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of . Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.

Suggested Citation

  • S. M. Sohel Rana & Umme Kulsum, 2017. "Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-11, July.
  • Handle: RePEc:hin:jnddns:9705985
    DOI: 10.1155/2017/9705985
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    Cited by:

    1. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Blé, Gamaliel & Dela-Rosa, Miguel Angel, 2019. "Neimark–Sacker bifurcation in a tritrophic model with defense in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 124-139.

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