A Fractional-Order Discrete Lorenz Map. (20th September 2022)

• Record Type: Journal Article
• Authors: Xie, Yanyun
• Other Names: tul Ain Qura Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2022(2022)
• Publication Date: 2022-09-20
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2022/2881207
• Languages: English
• ISSNs: 1687-9120

Abstract

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.