Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems

Recently, the fractional-order Chen–Lee system was proven to exhibit chaos by the presence of a positive Lyapunov exponent. However, the existence of chaos in fractional-order Chen–Lee systems has never been theoretically proven in the literature. Moreover, synchronization of chaotic fractional-orde...

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Bibliographic Details
Published in:Nonlinear dynamics 2010-12, Vol.62 (4), p.851-858
Main Authors: Chang, Ching-Ming, Chen, Hsien-Keng
Format: Article
Language:English
Subjects:
Automotive Engineering
Chaos theory
Classical Mechanics
Computer simulation
Control
Controllers
Dynamical Systems
Engineering
Existence theorems
Mathematical models
Mechanical Engineering
Nonlinear dynamics
Original Paper
Synchronism
Synchronization
Vibration
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Summary:Recently, the fractional-order Chen–Lee system was proven to exhibit chaos by the presence of a positive Lyapunov exponent. However, the existence of chaos in fractional-order Chen–Lee systems has never been theoretically proven in the literature. Moreover, synchronization of chaotic fractional-order systems was extensively studied through numerical simulations in some of the literature, but a theoretical analysis is still lacking. Therefore, we devoted ourselves to investigating the theoretical basis of chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems in this paper. Based on the stability theorems of fractional-order systems, the necessary conditions for the existence of chaos and the controllers for hybrid projective synchronization were derived. The numerical simulations show coincidence with the theoretical results.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-010-9767-6