Synchronization and anti-synchronization coexist in chaotic and hyperchaotic Chen–Lee systems

• Main Authors: Lin Yu-Kai, 林于凱
• Other Authors: Chen Juhn-Horng
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/22728532070283828677

碩士 === 中華大學 === 機械與航太工程研究所 === 95 === In this thesis, a new type of synchronization of chaos was presented. For some chaotic systems, synchronization and anti-synchronization can coexist in chaotic systems. This new type of synchronization is called “hybrid synchronization”. This study demonstrates that synchronization and anti-synchronization can coexist in the Chen-Lee chaotic systems by direct linear coupling. Based on the Lyapunov’s direct method, a linear controller was designed to assure coexistence of two different types of synchronization. In additions, the hybrid projective synchronizations of the chaotic and hyperchaotic Chen-Lee systems were also studied by using nonlinear control scheme. By utilizing the Lyapunov stability theory, the nonlinear controller was designed to guarantee the hybrid projective synchronization, which includes synchronization, anti-synchronization, and projective synchronization. Numerical examples were presented to validate the proposed approach. Finally, the dynamic behaviors of hyperchaotic Chen-Lee system with various fractional orders were investigated. It was found that the fractional orders play an important role on system’s dynamics. Results of this study show that coexistences of synchronization, anti-synchronization and the projective synchronization are attainable. Besides, complicated chaotic phenomena do occur in the fractional-order system. Keyword：Chen-Lee system, chaos synchronization, Lyapunov’s direct method, hyperchaotic system