Theoretical and experimental study of Chen chaotic system with notch filter feedback control

doi:10.1088/1674-1056/19/9/090507

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90507-090507.doi: 10.1088/1674-1056/19/9/090507

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

张晓明¹, 彭建华¹, 陈菊芳²

(1)College of Physics Science and Technology, Shenzhen University, Shenzhen 518060, China; (2)School of Physics, Northeast Normal University, Changchun 130024, China

收稿日期:2009-01-31 修回日期:2010-04-19 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 70571053, 10405018 and 10747147).

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Zhang Xiao-Ming(张晓明)^a), Chen Ju-Fang(陈菊芳)^b), and Peng Jian-Hua(彭建华)^a)^†

^a College of Physics Science and Technology, Shenzhen University, Shenzhen 518060, China; ^b School of Physics, Northeast Normal University, Changchun 130024, China

Received:2009-01-31 Revised:2010-04-19 Online:2010-09-15 Published:2010-09-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 70571053, 10405018 and 10747147).

摘要/Abstract

摘要： Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.

Abstract: Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.

Key words: notch filter feedback control, Chen chaotic system, Hopf bifurcation

中图分类号:

0545

张晓明, 陈菊芳, 彭建华. Theoretical and experimental study of Chen chaotic system with notch filter feedback control[J]. 中国物理B, 2010, 19(9): 90507-090507.

Zhang Xiao-Ming(张晓明), Chen Ju-Fang(陈菊芳), and Peng Jian-Hua(彭建华). Theoretical and experimental study of Chen chaotic system with notch filter feedback control[J]. Chin. Phys. B, 2010, 19(9): 90507-090507.

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Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

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