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Open AccessArticle

The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders

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Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Medina 42353, Saudi Arabia
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Department of Mathematics and Computer Science, University of Larbi Tebessi, Tebessa 12002, Algeria
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Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
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Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
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Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
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Author to whom correspondence should be addressed.
Entropy 2018, 20(9), 710; https://doi.org/10.3390/e20090710
Received: 25 August 2018 / Revised: 13 September 2018 / Accepted: 13 September 2018 / Published: 14 September 2018
This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings. View Full-Text
Keywords: fractional discrete chaos; entropy; projective synchronization; full state hybrid projective synchronization; generalized synchronization; inverse full state hybrid projective synchronization; inverse generalized synchronization fractional discrete chaos; entropy; projective synchronization; full state hybrid projective synchronization; generalized synchronization; inverse full state hybrid projective synchronization; inverse generalized synchronization
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Bendoukha, S.; Ouannas, A.; Wang, X.; Khennaoui, A.-A.; Pham, V.-T.; Grassi, G.; Huynh, V.V. The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders. Entropy 2018, 20, 710.

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