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

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

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.

Keywords: notch filter feedback control Chen chaotic system Hopf bifurcation

Received: 31 January 2009
Revised: 19 April 2010
Accepted manuscript online:

PACS:	0545
	0547

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 70571053, 10405018 and 10747147).

Cite this article:

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 2010 Chin. Phys. B 19 090507

[1]	Ahlborn A and Parlitz U 2006 Phys. Rev. Lett. 96 034102
[2]	Pyragas K 1992 Phys. Lett. A 170 421
[3]	Socolar J E S, Sukow D W and Gauthier D J 1994 Phys. Rev. E 50 3245
[4]	Gang H and Qu Z 1994 Phys. Rev. Lett. 72 68
[5]	Hu G, Xiao J, Chua L O and Pivka L 1998 Phys. Rev. Lett. 80 1884
[6]	Zhang X M, Peng J H and Zhang R Y 2005 Acta Phys. Sin. 54 3019 (in Chinese)
[7]	Boccaletti S, Grebogi C, Lai Y C, Mancini H and Maza D 2000 Phys. Rep. 329 103
[8]	Liu X W, Huang Q Z, Gao X and Shao S Q 2007 Chin. Phys. 16 2272
[9]	Li R H, Xue W and Li S 2007 Chin. Phys. 16 1591
[10]	Lu W G, Zhou L W and Luo Q M 2007 Chin. Phys. 16 3256
[11]	Wei D Q and Luo X S 2007 Chin. Phys. 16 3244
[12]	Wei D Q and Luo X S 2008 Chin. Phys. B 17 92
[13]	Feng Y L and Shen K 2008 Chin. Phys. B 17 111
[14]	Liu F, Guan Z H and Wang H 2008 Chin. Phys. B 17 2405
[15]	Ma J, Wang Q Y, Jin W Y and Xia Y F 2008 Chin. Phys. Lett. 25 3582
[16]	Oikawa N, Hidaka Y and Kai S 2008 Phys. Rev. E 77 035205
[17]	Tian L L, Li D H and Sun X F 2008 Chin. Phys. B 17 507
[18]	Yu H J, Bai L, Weng J Q and Luo X S 2008 Chin. Phys. Lett. 25 862
[19]	Zambrano S, Sanjuan M A F and Yorke J A 2008 Phys. Rev. E 77 055201
[20]	Gao J H, Xie L L, Zou W and Zhan M 2009 Phys. Rev. E 79 056214
[21]	Guo R W and Vincent U E 2009 Chin. Phys. Lett. 26 090506
[22]	Peng S G and Yu S M 2009 Chin. Phys. B 18 3758
[23]	Wei D Q and Zhang B 2009 Chin. Phys. B 18 1399
[24]	Xu J and Luo X B 2009 Chin. Phys. Lett. 26 040305
[25]	Zambrano S and Sanjuan M A F 2009 Phys. Rev. E 79 026217
[26]	Ouyang K J, Tang J S and Liang C X 2009 Chin. Phys. B 18 4748
[27]	Just W, Bernard T, Ostheimer M, Reibold E and Benner H 1997 Phys. Rev. Lett. 78 203
[28]	Ahlborn A and Parlitz U 2005 Phys. Rev. E 72 016206
[29]	Ahlborn A and Parlitz U 2007 Phys. Rev. E 75 065202
[30]	Zhang X M, Peng J H and Chen G R 2004 Acta Phys. Sin. 53 2864 (in Chinese)
[31]	Chen G R and Ueta T 1999 Int. J. Bifurcat Chaos 9 1465
[32]	Yu X H and Xia Y 2000 Int. J. Bifurcat Chaos 10 1987
[33]	Hassard B D, Kazrinoff N D and Wan Y H 1981 Theory and Applications of Hopf Bifurcation (Cambridge: Cambridge University Press) p86--90

[1]	Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[2]	The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation and coexisting attractors Yue Li(李月), Zengqiang Chen(陈增强), Mingfeng Yuan(袁明峰), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(6): 060503.
[3]	Transition to chaos in lid-driven square cavity flow Tao Wang(王涛) and Tiegang Liu(刘铁钢). Chin. Phys. B, 2021, 30(12): 120508.
[4]	The second Hopf bifurcation in lid-driven square cavity Tao Wang(王涛), Tiegang Liu(刘铁钢), Zheng Wang(王正). Chin. Phys. B, 2020, 29(3): 030503.
[5]	Nonlinear dynamics in non-volatile locally-active memristor for periodic and chaotic oscillations Wen-Yu Gu(谷文玉), Guang-Yi Wang(王光义), Yu-Jiao Dong(董玉姣), and Jia-Jie Ying(应佳捷). Chin. Phys. B, 2020, 29(11): 110503.
[6]	Hopf bifurcation control of a Pan-like chaotic system Liang Zhang(张良), JiaShi Tang(唐驾时), Qin Han(韩芩). Chin. Phys. B, 2018, 27(9): 094702.
[7]	Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium Jianghong Bao(鲍江宏), Dandan Chen(陈丹丹). Chin. Phys. B, 2017, 26(8): 080201.
[8]	Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback Liu Shuang (刘爽), Zhao Shuang-Shuang (赵双双), Wang Zhao-Long (王兆龙), Li Hai-Bin (李海滨). Chin. Phys. B, 2015, 24(1): 014501.
[9]	Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system Liu Shuang (刘爽), Zhao Shuang-Shuang (赵双双), Sun Bao-Ping (孙宝平), Zhang Wen-Ming (张文明). Chin. Phys. B, 2014, 23(9): 094501.
[10]	Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation Zhu Zhi-Wen (竺致文), Zhang Qing-Xin (张庆昕), Xu Jia (许佳). Chin. Phys. B, 2014, 23(8): 088201.
[11]	Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation Jia Bing (贾冰). Chin. Phys. B, 2014, 23(5): 050510.
[12]	Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance Chen Meng-Jiao (陈梦娇), Ling Heng-Li (令恒莉), Liu Yi-Hui (刘一辉), Qu Shi-Xian (屈世显), Ren Wei (任维). Chin. Phys. B, 2014, 23(2): 028701.
[13]	Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode Zhang Wei-Ya (张玮亚), Li Yong-Li (李永丽), Chang Xiao-Yong (常晓勇), Wang Nan (王楠). Chin. Phys. B, 2013, 22(9): 098401.
[14]	Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system Xue Wei (薛薇), Qi Guo-Yuan (齐国元), Mu Jing-Jing (沐晶晶), Jia Hong-Yan (贾红艳), Guo Yan-Ling (郭彦岭). Chin. Phys. B, 2013, 22(8): 080504.
[15]	Chaotic dynamic behavior analysis and control for a financial risk system Zhang Xiao-Dan (张晓丹), Liu Xiang-Dong (刘祥东), Zheng Yuan (郑媛), Liu Cheng (刘澄). Chin. Phys. B, 2013, 22(3): 030509.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention