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Entropy 2019, 21(4), 383;

Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability

School of Electronic and Information Engineering, Anshun University, Anshun 561000, China
School of Mathematics and Computer Science, Guizhou Education University, Guiyang 550018, China
School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China
Author to whom correspondence should be addressed.
Received: 18 February 2019 / Revised: 28 March 2019 / Accepted: 8 April 2019 / Published: 10 April 2019
(This article belongs to the Special Issue The Fractional View of Complexity)
PDF [5598 KB, uploaded 10 April 2019]


Compared with fractional-order chaotic systems with a large number of dimensions, three-dimensional or integer-order chaotic systems exhibit low complexity. In this paper, two novel four-dimensional, continuous, fractional-order, autonomous, and dissipative chaotic system models with higher complexity are revised. Numerical simulation of the two systems was used to verify that the two new fractional-order chaotic systems exhibit very rich dynamic behavior. Moreover, the synchronization method for fractional-order chaotic systems is also an issue that demands attention. In order to apply the Lyapunov stability theory, it is often necessary to design complicated functions to achieve the synchronization of fractional-order systems. Based on the fractional Mittag–Leffler stability theory, an adaptive, large-scale, and asymptotic synchronization control method is studied in this paper. The proposed scheme realizes the synchronization of two different fractional-order chaotic systems under the conditions of determined parameters and uncertain parameters. The synchronization theory and its proof are given in this paper. Finally, the model simulation results prove that the designed adaptive controller has good reliability, which contributes to the theoretical research into, and practical engineering applications of, chaos. View Full-Text
Keywords: fractional-order; chaotic system; Mittag–Leffler stability; adaptive laws fractional-order; chaotic system; Mittag–Leffler stability; adaptive laws

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Liu, L.; Du, C.; Zhang, X.; Li, J.; Shi, S. Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability. Entropy 2019, 21, 383.

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