A Fractional-Order Discrete Lorenz Map

Yanyun Xie and Qura tul Ain

Advances in Mathematical Physics, 2022, vol. 2022, 1-9

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:2881207

DOI: 10.1155/2022/2881207

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