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A Fractional‐Order Discrete Lorenz Map

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  • Yanyun Xie

Abstract

In this paper, a discrete Lorenz map with the fractional difference is analyzed. Bifurcations of the map in commensurate‐order and incommensurate‐order cases are studied when an order and a parameter are varied. Hopf bifurcation and periodic‐doubling cascade are found by the numerical simulations. The parameter values of Hopf bifurcation points are determined when the order is taken as a different value. It can be concluded that the parameter decreases as the order increases. Chaos control and synchronization for the fractional‐order discrete Lorenz map are studied through designing the suitable controllers. The effectiveness of the controllers is illustrated by numerical simulations.

Suggested Citation

  • Yanyun Xie, 2022. "A Fractional‐Order Discrete Lorenz Map," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:2881207
    DOI: 10.1155/2022/2881207
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    References listed on IDEAS

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    4. Ouannas, Adel & Khennaoui, Amina-Aicha & Odibat, Zaid & Pham, Viet-Thanh & Grassi, Giuseppe, 2019. "On the dynamics, control and synchronization of fractional-order Ikeda map," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 108-115.
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