中国物理B ›› 2011, Vol. 20 ›› Issue (8): 80505-080505.doi: 10.1088/1674-1056/20/8/080505

• GENERAL • 上一篇    下一篇

A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

司刚全, 孙志勇, 张彦斌   

  1. State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
  • 收稿日期:2011-01-19 修回日期:2011-03-13 出版日期:2011-08-15 发布日期:2011-08-15

A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

Si Gang-Quan(司刚全), Sun Zhi-Yong(孙志勇)†, and Zhang Yan-Bin(张彦斌)   

  1. State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2011-01-19 Revised:2011-03-13 Online:2011-08-15 Published:2011-08-15

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摘要： This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By introducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.

Abstract: This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By introducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.

Key words: chaos synchronization, integer-order chaotic system, fractional-order chaotic system, fractional calculus

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
05.45.Xt (Synchronization; coupled oscillators) 05.45.Gg (Control of chaos, applications of chaos)