0
Research Papers

Synchronization and Antisynchronization of a Class of Chaotic Systems With Nonidentical Orders and Uncertain Parameters

[+] Author and Article Information
Diyi Chen

Department of Electrical Engineering,
Northwest A&F University,
Shaanxi, Yangling 712100, China

Weili Zhao

School of Electrical Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi 710049, China

Xinzhi Liu

Department of Applied Mathematics,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada

Xiaoyi Ma

Department of Electrical Engineering,
Northwest A&F University,
Shaanxi, Yangling 712100, China
e-mail: ieee307@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 21, 2012; final manuscript received May 22, 2013; published online September 12, 2014. Assoc. Editor: Claude-Henri Lamarque.

J. Comput. Nonlinear Dynam 10(1), 011003 (Sep 12, 2014) (8 pages) Paper No: CND-12-1094; doi: 10.1115/1.4027715 History: Received June 21, 2012; Revised May 22, 2013

In this paper, we study the synchronization of a class of uncertain chaotic systems. Based on the sliding mode control and stability theory in fractional calculus, a new controller is designed to achieve synchronization. Examples are presented to illustrate the effectiveness of the proposed controller, like the synchronization between an integer-order system and a fraction-order system, the synchronization between two fractional-order hyperchaotic systems (FOHS) with nonidentical fractional orders, the antisynchronization between an integer-order system and a fraction-order system, the synchronization between two new nonautonomous systems. The simulation results are in good agreement with the theory analysis and it is noted that the proposed control method is of vital importance for practical system parameters are uncertain and imprecise.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Phase diagram of integer-order and fraction-order chaotic Liu systems (β1 = β2 = β3 = 0.95)

Grahic Jump Location
Fig. 2

Synchronization errors between integer-order and fraction-order chaotic Liu systems (e1=x2-x1,e2=y2-y1,e3=z2-z1)

Grahic Jump Location
Fig. 3

Chaotic attractors of 4D fraction-order Lü FOHS with nonidentical orders (α1 = α2 = α3 = α4 = 0.90, β1 = β2 = β3 = β4 = 0.95)

Grahic Jump Location
Fig. 4

Synchronization errors between 4D fraction-order systems with nonidentical orders (e1 = x2-x1,e2 = y2-y1,e3 = z2-z1,e4 = w2-w1)

Grahic Jump Location
Fig. 6

Trajectories of the states in drive and response Lorenz systems

Grahic Jump Location
Fig. 7

Antisynchronization errors between integer-order and fraction-order chaotic Lorenz systems (e1 = x1+x2,e2 = y1+y2,e3 = z1+z2)

Grahic Jump Location
Fig. 9

Synchronization errors between new integer-order and fraction-order chaotic nonautonomous Chen systems (e1=x2-x1,e2 = y2-y1,e3 = z2-z1)

Grahic Jump Location
Fig. 8

Phase diagram of new integer-order and fraction-order chaotic nonautonomous Chen systems (β1 = β2 = β3 = 0.95)

Grahic Jump Location
Fig. 5

Chaotic attractors of integer-order and fraction-order chaotic Lorenz systems

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In