On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization
Amina-Aicha Khennaoui,
Adel Ouannas,
Samir Bendoukha,
Xiong Wang,
Viet-Thanh Pham
Affiliations
Amina-Aicha Khennaoui
Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Adel Ouannas
Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria
Samir Bendoukha
Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Medina 42353, Saudi Arabia
Xiong Wang
Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
Viet-Thanh Pham
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
In this paper, we propose a fractional map based on the integer-order unified map. The chaotic behavior of the proposed map is analyzed by means of bifurcations plots, and experimental bounds are placed on the parameters and fractional order. Different control laws are proposed to force the states to zero asymptotically and to achieve the complete synchronization of a pair of fractional unified maps with identical or nonidentical parameters. Numerical results are used throughout the paper to illustrate the findings.
