Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 120507-120507.doi: 10.1088/1674-1056/21/12/120507

• GENERAL • 上一篇    下一篇

Synchronization between a novel class of fractional-order and integer-order chaotic systems via sliding mode controller

陈帝伊, 张润凡, 马孝义, 王娟   

  1. Department of Electrical Engineering, College of Water Resources and Architectural Engineering, Northwest Agriculture & Forestry University, Yangling 712100, China
  • 收稿日期:2012-02-25 修回日期:2012-06-11 出版日期:2012-11-01 发布日期:2012-11-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 51109180).

Synchronization between a novel class of fractional-order and integer-order chaotic systems via sliding mode controller

Chen Di-Yi (陈帝伊), Zhang Run-Fan (张润凡), Ma Xiao-Yi (马孝义), Wang Juan (王娟)   

  1. Department of Electrical Engineering, College of Water Resources and Architectural Engineering, Northwest Agriculture & Forestry University, Yangling 712100, China
  • Received:2012-02-25 Revised:2012-06-11 Online:2012-11-01 Published:2012-11-01
  • Contact: Ma Xiao-Yi E-mail:ieee307@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 51109180).

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摘要： In order to figure out the dynamical behaviours of fractional-order chaotic system and its relation to integer-order chaotic system, in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method. Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus. Moreover, three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results. Finally, results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.

关键词: synchronization, fractional-order system, integer-order chaotic system, sliding mode

Abstract: In order to figure out the dynamical behaviours of fractional-order chaotic system and its relation to integer-order chaotic system, in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method. Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus. Moreover, three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results. Finally, results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.

Key words: synchronization, fractional-order system, integer-order chaotic system, sliding mode

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
02.30.Uu (Integral transforms) 02.60.Cb (Numerical simulation; solution of equations) 05.45.Pq (Numerical simulations of chaotic systems)