Synchronization of fractional chaotic systems based on a simple Lyapunov function

Advances in Difference Equations

Yu Wang¹  Chao Zhao²  Tianzeng Li² 

[1] Artificial Intelligence Key Laboratory of Sichuan Province, Zigong, China;School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China

关键词: Lyapunov function;    fractional order;    synchronization;    chaos;   

DOI  :  10.1186/s13662-017-1320-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper the synchronization of fractional-order chaotic systems and a new property of fractional derivatives are studied. Then we propose a new fractional-order extension of Lyapunov direct method to control the fractional-order chaotic systems. A new synchronization method and a linear feedback controller are given to achieve the synchronization of fractional-order chaotic systems based on a simple Lyapunov candidate function. The proposed synchronization method can be applied to the synchronization of an arbitrary fractional-order chaotic system. This method is universal, simple, and theoretically rigorous. Numerical simulations of three fractional-order chaotic systems to verify the effectiveness and the universality of the proposed method.

【 授权许可】

CC BY