A new hyper-chaotic system and its synchronization

This paper presents a new hyper-chaotic system obtained by adding a nonlinear controller to the third equation of the three-dimensional autonomous Chen–Lee chaotic system. Computer simulations demonstrated the hyper-chaotic dynamic behaviors of the system. Numerical results revealed that the new hyp...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2009-08, Vol.10 (4), p.2088-2096
Main Authors: Chen, Cheng-Hsien, Sheu, Long-Jye, Chen, Hsien-Keng, Chen, Juhn-Horng, Wang, Hung-Chih, Chao, Yi-Chi, Lin, Yu-Kai
Format: Article
Language:English
Subjects:
Chen–Lee system
Hybrid projective synchronization
Hyper-chaos
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Summary:This paper presents a new hyper-chaotic system obtained by adding a nonlinear controller to the third equation of the three-dimensional autonomous Chen–Lee chaotic system. Computer simulations demonstrated the hyper-chaotic dynamic behaviors of the system. Numerical results revealed that the new hyper-chaotic system possesses two positive exponents. It was also found that the structure of the hyper-chaotic attractors is more complex than those of the Chen–Lee chaotic system. Furthermore, the hybrid projective synchronization (HPS) of the new hyper-chaotic systems was studied using a nonlinear feedback control. The nonlinear controller was designed according to Lyapunov’s direct method to guarantee HPS, which includes synchronization, anti-synchronization, and projective synchronization. Numerical examples are presented in order to illustrate HPS.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2008.03.015