New type of chaos synchronization in discrete-time systems: the F-M synchronization

Open Physics

Ziar Toufik¹  Karouma Abdulrahman²  Ouannas Adel³  Grassi Giuseppe⁴  Wang Xiong⁵  Pham Viet–Thanh⁶ 

[1] Department of Material Sciences, University Larbi Tebessi, Tebessa, 12002Algeria;Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada;Department of Mathematics, University of Larbi Tebessi, Tebessa, 12002, Algeria;Dipartimento Ingegneria Innovazione, Universitá del Salento, 73100Lecce, Italy;Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, P.R, China;Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam;

关键词: inverse generalized synchronization;    matrix projective synchronization;    chaotic systems;    discrete-time systems;    lyapunov stability theory;    05.45.gg;    05.45.xt;   

DOI  :  10.1515/phys-2018-0025

来源: DOAJ

【 摘 要 】

In this paper, a new type of synchronization for chaotic (hyperchaotic) maps with different dimensions is proposed. The novel scheme is called F – M synchronization, since it combines the inverse generalized synchronization (based on a functional relationship F) with the matrix projective synchronization (based on a matrix M). In particular, the proposed approach enables F – M synchronization with index d to be achieved between n-dimensional drive system map and m-dimensional response system map, where the synchronization index d corresponds to the dimension of the synchronization error. The technique, which exploits nonlinear controllers and Lyapunov stability theory, proves to be effective in achieving the F – M synchronization not only when the synchronization index d equals n or m, but even if the synchronization index d is larger than the map dimensions n and m. Finally, simulation results are reported, with the aim to illustrate the capabilities of the novel scheme proposed herein.

【 授权许可】

Unknown