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

doi:10.1088/1674-1056/19/12/120507

中国物理B ›› 2010, Vol. 19 ›› Issue (12): 120507-120507.doi: 10.1088/1674-1056/19/12/120507

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

牛玉军, 王兴元, 年福忠, 王明军

School of Electronic & Information Engineering, Dalian University of Technology, Dalian 116024, China

收稿日期:2010-04-29 修回日期:2010-07-01 出版日期:2010-12-15 发布日期:2010-12-15
基金资助:
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), and the Natural Science Foundation of Liaoning Province, China (Grant No. 20082165).

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

Niu Yu-Jun(牛玉军), Wang Xing-Yuan(王兴元)^†, Nian Fu-Zhong(年福忠), and Wang Ming-Jun(王明军)

School of Electronic & Information Engineering, Dalian University of Technology, Dalian 116024, China

Received:2010-04-29 Revised:2010-07-01 Online:2010-12-15 Published:2010-12-15
Supported by:
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), and the Natural Science Foundation of Liaoning Province, China (Grant No. 20082165).

摘要/Abstract

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.

Abstract: 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.

Key words: dynamic analysis, fractional order, generalized projective synchronization, Laplace transformation

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

05.45.Pq (Numerical simulations of chaotic systems) 05.45.Xt (Synchronization; coupled oscillators)

牛玉军, 王兴元, 年福忠, 王明军. Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization[J]. 中国物理B, 2010, 19(12): 120507-120507.

Niu Yu-Jun(牛玉军), Wang Xing-Yuan(王兴元), Nian Fu-Zhong(年福忠), and Wang Ming-Jun(王明军). Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization[J]. Chin. Phys. B, 2010, 19(12): 120507-120507.

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

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

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