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Stability, bifurcation and chaos control of a discretized Leslie prey-predator model

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  • Akhtar, S.
  • Ahmed, R.
  • Batool, M.
  • Shah, Nehad Ali
  • Chung, Jae Dong

Abstract

For a variety of purposes, discrete-time models are superior to continuous-time models. Many techniques are introduced to discretize continuous-time models. In this paper, a non-standard finite difference scheme is used to discretize a continuous-time Leslie prey-predator model. We study the local stability of the fixed points and Neimark-Sacker bifurcation at the positive fixed point. Moreover, hybrid control technique is used to control chaos and bifurcation in the model at the positive fixed point. Numerical simulations are provided to illustrate the theoretical discussion.

Suggested Citation

  • Akhtar, S. & Ahmed, R. & Batool, M. & Shah, Nehad Ali & Chung, Jae Dong, 2021. "Stability, bifurcation and chaos control of a discretized Leslie prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006998
    DOI: 10.1016/j.chaos.2021.111345
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    References listed on IDEAS

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    1. A. Q. Khan, 2020. "Neimark–Sacker Bifurcation of a Two-Dimensional Discrete-Time Chemical Model," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, August.
    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. Isnani Darti & Agus Suryanto, 2020. "Dynamics of a SIR Epidemic Model of Childhood Diseases with a Saturated Incidence Rate: Continuous Model and Its Nonstandard Finite Difference Discretization," Mathematics, MDPI, vol. 8(9), pages 1-13, August.
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