A simple method to simultaneously achieve synchronization andanti-synchronization in chaotic systems

doi:10.1088/1674-1056/19/1/010508

中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10508-010508.doi: 10.1088/1674-1056/19/1/010508

A simple method to simultaneously achieve synchronization andanti-synchronization in chaotic systems

李瑞红¹, 陈为胜¹, 李爽²

(1)Department of Applied Mathematics, Xidian University, Xi'an 710071, China; (2)School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, China

收稿日期:2009-04-29 修回日期:2009-06-12 出版日期:2010-01-15 发布日期:2010-01-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60804021).

A simple method to simultaneously achieve synchronization and anti-synchronization in chaotic systems

Li Rui-Hong(李瑞红)^a)†, Chen Wei-Sheng(陈为胜)^a), and Li Shuang(李爽)^b)

^a Department of Applied Mathematics, Xidian University, Xi'an 710071, China; ^b School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, China

Received:2009-04-29 Revised:2009-06-12 Online:2010-01-15 Published:2010-01-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60804021).

摘要/Abstract

摘要： In this paper, a novel adaptive control approach is presented to simultaneously achieve synchronization and anti-synchronization in partially linear chaotic systems. Through appropriately separating state vectors of such systems, synchronization and anti-synchronization could be simultaneously realized in different subspaces, which may be strictly proven theoretically. Simulation results for a Lorenz chaotic system and a new hyper-chaotic system are provided to illustrate the effectiveness of the proposed method. Finally, a new secure communication scheme based on such a synchronization phenomenon of the hyper-chaotic system is demonstrated. Numerical results show success in transmitting a periodic signal with high security.

Abstract: In this paper, a novel adaptive control approach is presented to simultaneously achieve synchronization and anti-synchronization in partially linear chaotic systems. Through appropriately separating state vectors of such systems, synchronization and anti-synchronization could be simultaneously realized in different subspaces, which may be strictly proven theoretically. Simulation results for a Lorenz chaotic system and a new hyper-chaotic system are provided to illustrate the effectiveness of the proposed method. Finally, a new secure communication scheme based on such a synchronization phenomenon of the hyper-chaotic system is demonstrated. Numerical results show success in transmitting a periodic signal with high security.

Key words: synchronization and anti-synchronization, adaptive control, secure communication

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems)

李瑞红, 陈为胜, 李爽. A simple method to simultaneously achieve synchronization andanti-synchronization in chaotic systems[J]. 中国物理B, 2010, 19(1): 10508-010508.

Li Rui-Hong(李瑞红), Chen Wei-Sheng(陈为胜), and Li Shuang(李爽) . A simple method to simultaneously achieve synchronization and anti-synchronization in chaotic systems[J]. Chin. Phys. B, 2010, 19(1): 10508-010508.

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A simple method to simultaneously achieve synchronization andanti-synchronization in chaotic systems

A simple method to simultaneously achieve synchronization and anti-synchronization in chaotic systems

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