Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization  

作　　者：牛玉军 王兴元 年福忠 王明军 

机构地区：[1]School of Electronic & Information Engineering,Dalian University of Technology

出　　处：《Chinese Physics B》2010年第12期97-104,共8页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152);the Doctoral Program Foundation of Institution of Higher Education of China (Grant No. 20070141014);the Natural Science Foundation of Liaoning Province,China (Grant No. 20082165)

摘　　要：Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory.Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory.

关 键 词：dynamic analysis fractional order generalized projective synchronization Laplace transformation 

分 类 号：O415.5[理学—理论物理] TP273[理学—物理]