A new hyper-chaotic system and its synchronization |
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| Authors: | Cheng-Hsien Chen Long-Jye Sheu Hsien-Keng Chen Juhn-Horng Chen Hung-Chih Wang Yi-Chi Chao Yu-Kai Lin |
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| Institution: | 1. Department of Vehicle Engineering, Army Academy ROC, Taoyuan, Taiwan;2. Department of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan;3. Department of Industrial Engineering & Management, Hsiuping Institute of Technology, Taichung, Taiwan;4. Department of Mechanical Engineering, Hsiuping Institute of Technology, Taichung, Taiwan |
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| Abstract: | 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. |
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