Different dimensional fractional-order discrete chaotic systems based on the Caputo h -difference discrete operator: dynamics, control, and synchronization

Advances in Difference Equations

article

Talbi, Ibtissem¹  Ouannas, Adel²  Khennaoui, Amina-Aicha³  Berkane, Abdelhak¹  Batiha, Iqbal M.⁴  Grassi, Giuseppe⁵  Pham, Viet-Thanh⁶ 

[1] Department of Mathematics, University of Constantine;Department of Mathematics and Computer Science, University of Larbi Ben M’hidi;Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi;Department of Mathematics, Faculty of Science, University of Jordan;Dipartimento Ingegneria Innovazione, Universita del Salento;Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University

关键词: Discrete fractional calculus;    Control;    Synchronization;    Discrete Lorenz system;    Discrete Wang system;    Lyapunov approach;   

DOI  :  10.1186/s13662-020-03086-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wang Discrete System (3D-FoWDS). Then, some novel theorems based on the Lyapunov approach are proved, with the aim of controlling and synchronizing the map dynamics. In particular, a new hybrid scheme is proposed, which enables synchronization to be achieved between a master system based on a 2D-FoLDS and a slave system based on a 3D-FoWDS. Simulation results are reported to highlight the effectiveness of the conceived approach.

【 授权许可】

CC BY