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In this paper, nonfeedback chaos control of Chens system is realized with nonresonant parametric drive. A periodic signal whose frequency is far higher than the systems mean frequency is used as the input. And the system variables of the controlled system are decomposed into slowly varying variables which change according to the systems mean frequency and fast varying variables which change according to the frequency of periodic signal. Then, by averaging method, a slowly varying dynamics is obtained. According to the dynamical characteristics of the slowly varying dynamics, the available control parameter range is obtained. Numerical simulation results show that this method can lead the controlled system to the target state rapidly, even when the control signal is disturbed by noise in certain SNR ranges, so the proposed method is feasible.
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Keywords:
- averaging method /
- Chens system /
- chaotic control
[1] Hu G, Xiao J H, Zhen Z G 2000 Chaos Control (1st ed) (Shanghai: Shanghai Scientific and Technological Education Publishing House) p8 (in Chinese) [胡 岗、萧井华、郑志刚 2000 混沌控制 (第1版) (上海: 上海科技教育出版社) 第8页]
[2] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. lett. 64 1196
[3] Lima R, Pettini M 1990 Phys. Rev. B 41 726
[4] Yang C Y, Tang G N 2009 Acta Phys. Sin. 58 143 (in Chinese) [杨朝羽、唐国宁 2009 物理学报 58 143]
[5] Chen G P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) [陈光平、郝加波 2009 物理学报 58 2914]
[6] Li D, Zhang X H, Yang D, Wang S L 2009 Acta Phys. Sin. 58 1432 (in Chinese) [李 东、张小洪、杨 丹、王时龙 2009 物理学报 58 1432]
[7] Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) [王校锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3729]
[8] Zhang L P, Jiang H B, Bi Q S 2010 Chin. Phys. B 19 010507
[9] Li R H, Chen W S, Li S 2010 Chin. Phys. B 19 010508
[10] Li D, Wang S L, Zhang X H, Yang D 2010 Chin.Phys. B 19 010506
[11] Wu S H, Hao J H, Xu H B 2010 Chin. Phys. B 19 020509
[12] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 0140 (in Chinese) [行鸿彦、金天力 2010 物理学报 59 0140]
[13] Soong C Y, Huang W T, Lin F P, Tzeng P Y 2004 Phys. Rev. E 70 0162111
[14] Choe C U, Hohne K, Benner H, Kivshar Y S 2005 Phys. Rev. E 72 0362061
[15] Chen G R, Ueta T 1999 Int. J. Bifurcation Chaos 9 1465
[16] Ueta T, Chen G R 2000 Int. J. Bifurcation Chaos 10 1917
[17] Park E H, Zaks M A, Kurths J 1999 Phys. Rev. E 60 6627
[18] Chen L, Wang D S 2007 Acta Phys. Sin. 56 91 (in Chinese) [谌 龙、王德石 2007 物理学报 56 91]
[19] Liu Y Z, Chen L Q 2001 Nonlinear Vibrations (1st ed) (Beijing: High Education Press) pp73-82 (in Chinese) [刘延柱、陈立群 2001 非线性振动 (第1版) (北京: 高等教育出版社) 第73—第82页]
[20] Kivshar Y S, Rodelsperger F, Benner H 1994 Phys. Rev. E 49 319
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[1] Hu G, Xiao J H, Zhen Z G 2000 Chaos Control (1st ed) (Shanghai: Shanghai Scientific and Technological Education Publishing House) p8 (in Chinese) [胡 岗、萧井华、郑志刚 2000 混沌控制 (第1版) (上海: 上海科技教育出版社) 第8页]
[2] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. lett. 64 1196
[3] Lima R, Pettini M 1990 Phys. Rev. B 41 726
[4] Yang C Y, Tang G N 2009 Acta Phys. Sin. 58 143 (in Chinese) [杨朝羽、唐国宁 2009 物理学报 58 143]
[5] Chen G P, Hao J B 2009 Acta Phys. Sin. 58 2914 (in Chinese) [陈光平、郝加波 2009 物理学报 58 2914]
[6] Li D, Zhang X H, Yang D, Wang S L 2009 Acta Phys. Sin. 58 1432 (in Chinese) [李 东、张小洪、杨 丹、王时龙 2009 物理学报 58 1432]
[7] Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729 (in Chinese) [王校锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3729]
[8] Zhang L P, Jiang H B, Bi Q S 2010 Chin. Phys. B 19 010507
[9] Li R H, Chen W S, Li S 2010 Chin. Phys. B 19 010508
[10] Li D, Wang S L, Zhang X H, Yang D 2010 Chin.Phys. B 19 010506
[11] Wu S H, Hao J H, Xu H B 2010 Chin. Phys. B 19 020509
[12] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 0140 (in Chinese) [行鸿彦、金天力 2010 物理学报 59 0140]
[13] Soong C Y, Huang W T, Lin F P, Tzeng P Y 2004 Phys. Rev. E 70 0162111
[14] Choe C U, Hohne K, Benner H, Kivshar Y S 2005 Phys. Rev. E 72 0362061
[15] Chen G R, Ueta T 1999 Int. J. Bifurcation Chaos 9 1465
[16] Ueta T, Chen G R 2000 Int. J. Bifurcation Chaos 10 1917
[17] Park E H, Zaks M A, Kurths J 1999 Phys. Rev. E 60 6627
[18] Chen L, Wang D S 2007 Acta Phys. Sin. 56 91 (in Chinese) [谌 龙、王德石 2007 物理学报 56 91]
[19] Liu Y Z, Chen L Q 2001 Nonlinear Vibrations (1st ed) (Beijing: High Education Press) pp73-82 (in Chinese) [刘延柱、陈立群 2001 非线性振动 (第1版) (北京: 高等教育出版社) 第73—第82页]
[20] Kivshar Y S, Rodelsperger F, Benner H 1994 Phys. Rev. E 49 319
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