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Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model

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  • Qamar Din
  • A. A. Elsadany
  • Hammad Khalil

Abstract

This work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation for positive equilibrium with the help of an explicit criterion for Neimark-Sacker bifurcation. The chaos control in the model is discussed through implementation of two feedback control strategies, that is, pole-placement technique and hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the model.

Suggested Citation

  • Qamar Din & A. A. Elsadany & Hammad Khalil, 2017. "Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-15, April.
    • Handle: RePEc:hin:jnddns:6312964
    DOI: 10.1155/2017/6312964
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    Cited by:

    1. Din, Qamar, 2021. "Dynamics and chaos control for a novel model incorporating plant quality index and larch budmoth interaction," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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