Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control

• Published in: Nonlinear dynamics Vol. 70; no. 2; pp. 1549 - 1561
• Main Authors: Chen, Diyi, Zhang, Runfan, Clinton Sprott, Julien, Ma, Xiaoyi
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2012; Springer Nature B.V
• Subjects: Automotive Engineering; Chaos theory; Classical Mechanics; Control; Dynamical Systems; Engineering; Fuzzy control; Fuzzy systems; Initial conditions; Integers; Lorenz system; Mechanical Engineering; Original Paper; Sliding mode control; Synchronism; Vibration; Chaos synchronization; Fuzzy sliding mode control; Fractional-order chaotic system; Integer-order chaotic system
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-012-0555-3

In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new fuzzy sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Lü chaotic system and an integer-order Liu chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order hyperchaotic system based upon the Lorenz system, and the synchronization between a fractional-order hyperchaotic system based on Chen’s system, and an integer-order Liu chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.