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

Entropy

Chuanhong Du¹  Licai Liu¹  Shuaishuai Shi²  Xiefu Zhang³  Jian Li³ 

[1] School of Electronic and Information Engineering, Anshun University, Anshun 561000, China;School of Information Engineering, Guizhou University of Engineering Science, Bijie 551700, China;School of Mathematics and Computer Science, Guizhou Education University, Guiyang 550018, China;

关键词: fractional-order;    chaotic system;    Mittag–Leffler stability;    adaptive laws;   

DOI  :  10.3390/e21040383

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown