Next Article in Journal
Automatic Analysis of Archimedes’ Spiral for Characterization of Genetic Essential Tremor Based on Shannon’s Entropy and Fractal Dimension
Next Article in Special Issue
Research Frontier in Chaos Theory and Complex Networks
Previous Article in Journal
Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature
Previous Article in Special Issue
Inferring the Population Mean with Second-Order Information in Online Social Networks
Open AccessArticle

On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization

1
Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
2
Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria
3
Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Medina 42353, Saudi Arabia
4
Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
5
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(7), 530; https://doi.org/10.3390/e20070530
Received: 9 June 2018 / Revised: 11 July 2018 / Accepted: 12 July 2018 / Published: 15 July 2018
(This article belongs to the Special Issue Research Frontier in Chaos Theory and Complex Networks)
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. View Full-Text
Keywords: fractional unified map; unified map; fractional discrete calculus; chaos control; chaos synchronization fractional unified map; unified map; fractional discrete calculus; chaos control; chaos synchronization
Show Figures

Figure 1

MDPI and ACS Style

Khennaoui, A.-A.; Ouannas, A.; Bendoukha, S.; Wang, X.; Pham, V.-T. On Chaos in the Fractional-Order Discrete-Time Unified System and Its Control Synchronization. Entropy 2018, 20, 530.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop