Synchronization of fractional-order and integer-order chaotic (hyper-chaotic) systems with different dimensions

• Main Authors: Xiaoyan Yang, Heng Liu, Shenggang Li
• Format: Article
• Language: English
• Published: SpringerOpen 2017-10-01
• Series: Advances in Difference Equations
• Subjects: W − Λ ( t ) $W-\Lambda(t)$ synchronization; fractional-order system; scaling matrix; chaotic (hyper-chaotic) system
• Online Access: http://link.springer.com/article/10.1186/s13662-017-1399-4

Abstract By constructing two scaling matrices, i.e., a function matrix Λ ( t ) $\Lambda (t)$ and a constant matrix W which is not equal to the identity matrix, a kind of W − Λ ( t ) $W-\Lambda(t)$ synchronization between fractional-order and integer-order chaotic (hyper-chaotic) systems with different dimensions is investigated in this paper. Based on the fractional-order Lyapunov direct method, a controller is designed to drive the synchronization error convergence to zero asymptotically. Finally, four numerical examples are presented to illustrate the effectiveness of the proposed method.