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中国物理学会期刊

分数阶Liu系统与分数阶统一系统中的混沌现象及二者的异结构同步

CSTR: 32037.14.aps.56.5124

Chaos in fractional-order Liu system and a fractional-order unified system and the synchronization between them

CSTR: 32037.14.aps.56.5124
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  • 对近几年提出的Liu混沌系统和统一混沌系统,研究了其分数阶系统的混沌动力学行为,发现低于三阶的两系统均存在混沌吸引子,且存在混沌的最低阶数仅为0.3,并计算了存在混沌时系统的最大Lyapunov指数,证明了混沌的存在性;利用Active控制技术实现了分数阶Liu系统与分数阶Lorenz系统及分数阶Lü系统的异结构同步.理论分析及数值实验都证明了该同步方案的有效性.

     

    This paper studies the chaotic behaviors of the fractional-order Liu system and the fractional-order unified system which were presented several years ago. It is found that chaos exists in the both systems with order less than three and the lowest order to have chaos is 0.3. The calculation results of the maximum Lyapunov exponents when the system is chaotic illustrate the existence of chaos. Chaos synchronization between fractional-order Liu system, fractional-order Lorenz system and fractional-order Lü sytem is realized by employing active control technique. Theoretieal analysis and numerical simulations demonstrate the effectiveness of the proposed method.

     

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