-
A linear delayed position feedback is introduced into a Helmholtz oscillator system, and its effects on controlling the erosion of safe basins are investigated. The condition of fractal erosion of the basin boundary of the delayed feedback controlled system is acquired, there by the threshold of the excitation of the fractal erosion is obtained. Then considering time delay as a variable parameter and employing the 4th-order Runge-Kutta method and the point-to-point mapping method, evolutions of safe basins with time delay are presented. It is found that the increasing of time delay can enhance the threshold of the fractal erosion and reduce the erosion of safe basin effectively under a weak feedback gain. All the results imply that delayed position feedback can be used as a good strategy to control the erosion of safe basins.
-
Keywords:
- safe basin /
- fractal erosion /
- time delay /
- feedback
[1] Thompson J M T, Rainey F C T, Soliman M S 1995 Philosophical Transactions of the Royal Society 332 149
[2] Wang D J, Yu L 2004 Journal of Ship Mechanics 8 25(in Chinese) [王冬姣、于 玲 2004 船舶力学 8 25]
[3] Soliman M S 1995 Journal of Sound and Vibration 182 618
[4] Senjanovic I, Parunov J, Cipric G 1997 Chaos, Solitons and Fractals 4 659
[5] Xu J, Lu Q S, Huang K L 1996 Acta Mechanica Sinica 12 281
[6] Gan C B 2006 Chaos, Solitons and Fractals 30 920
[7] Rega G, Lenci S 2005 Nonlinear Analysis 63 902
[8] Rong H W, Wang X D, Xu W, Fang T 2008 Journal of Sound and Vibration 313 46
[9] Rong H W, Wang X D, Xu W, Fang T 2007 Acta Phys. Sin. 56 2005 (in Chinese)[戎海武、王向东、徐 伟、方 同 2007 56 2005]
[10] Rong H W, Wang X D, Xu W, Fang T 2008 Acta Phys. Sin. 57 1506 (in Chinese) [戎海武、王向东、徐 伟、方 同 2008 57 1506]
[11] Rong H W, Wang X D, Xu W, Fang T 2005 Acta Phys. Sin. 54 4610 (in Chinese) [戎海武、王向东、徐 伟、方 同 2005 物 理学报 54 4610] 〖12] Gong P L, Xu J X, Sun Z C 2001 Acta Phys. Sin. 50 841(in Chinese) [龚璞林、徐健学、孙政策 2001 50 841]
[12] Zhang Q, Wang B H, Yang C W 2005 Power System Technology 29 63(in Chinese)[张 强、 王宝华、 杨成梧 2005 电网技术 29 63] 〖14] Marcos S H C, Lopes S R, Viana R L 2003 Chaos, Solutions and Fractals 15 417
[13] Long Z J, Lee S K, Kim J Y 2010 Ocean Engineering 37 418
[14] Gu J Y, Miao Z H 2005 Journal of Jiangsu University of Science and Technology(Nature Science Edition) 19 6 (in Chinese)[谷家扬、缪振华 2005 江苏科技大学学报(自然科学版) 19 6]
[15] Ji G, Zhang W K 2002 Ship Building of China 43 25(in Chinese)[纪 刚、张纬康 2002 中国造船 43 25]
[16] Lewis C P, Uar A, Bishop S R 1998 Transactions of the Institute of Measurement and Control 20 29
[17] Nbendjo B R N, Salissou Y, Woafo P 2005 Chaos, Solitons and Fractals 23 809
[18] Shang H L, Xu J 2009 Chaos, Solitons and Fractals 41 1880
[19] Soliman M S, Thompson J M T 1989 Journal of Sound and Vibration 35 453
[20] Shang H L, Xu J 2008 Journal of Tongji University (Natural Science) 36 962(in Chinese)[尚慧琳、徐 鉴 2008同济大学 学报 36 962] 〖23] Qian Q,Wang L, Ni Q 2008 Chin. Phys. B 17 569
[21] Zou S C, Xu W, Jin Y F 2008 Acta Phys. Sin. 57 7527(in Chinese) [邹少存、徐 伟、靳艳飞 2008 57 7527]
[22] Tatlier M, enatalar A E 2001 Chaos, Solitons and Fractals 12 1145
-
[1] Thompson J M T, Rainey F C T, Soliman M S 1995 Philosophical Transactions of the Royal Society 332 149
[2] Wang D J, Yu L 2004 Journal of Ship Mechanics 8 25(in Chinese) [王冬姣、于 玲 2004 船舶力学 8 25]
[3] Soliman M S 1995 Journal of Sound and Vibration 182 618
[4] Senjanovic I, Parunov J, Cipric G 1997 Chaos, Solitons and Fractals 4 659
[5] Xu J, Lu Q S, Huang K L 1996 Acta Mechanica Sinica 12 281
[6] Gan C B 2006 Chaos, Solitons and Fractals 30 920
[7] Rega G, Lenci S 2005 Nonlinear Analysis 63 902
[8] Rong H W, Wang X D, Xu W, Fang T 2008 Journal of Sound and Vibration 313 46
[9] Rong H W, Wang X D, Xu W, Fang T 2007 Acta Phys. Sin. 56 2005 (in Chinese)[戎海武、王向东、徐 伟、方 同 2007 56 2005]
[10] Rong H W, Wang X D, Xu W, Fang T 2008 Acta Phys. Sin. 57 1506 (in Chinese) [戎海武、王向东、徐 伟、方 同 2008 57 1506]
[11] Rong H W, Wang X D, Xu W, Fang T 2005 Acta Phys. Sin. 54 4610 (in Chinese) [戎海武、王向东、徐 伟、方 同 2005 物 理学报 54 4610] 〖12] Gong P L, Xu J X, Sun Z C 2001 Acta Phys. Sin. 50 841(in Chinese) [龚璞林、徐健学、孙政策 2001 50 841]
[12] Zhang Q, Wang B H, Yang C W 2005 Power System Technology 29 63(in Chinese)[张 强、 王宝华、 杨成梧 2005 电网技术 29 63] 〖14] Marcos S H C, Lopes S R, Viana R L 2003 Chaos, Solutions and Fractals 15 417
[13] Long Z J, Lee S K, Kim J Y 2010 Ocean Engineering 37 418
[14] Gu J Y, Miao Z H 2005 Journal of Jiangsu University of Science and Technology(Nature Science Edition) 19 6 (in Chinese)[谷家扬、缪振华 2005 江苏科技大学学报(自然科学版) 19 6]
[15] Ji G, Zhang W K 2002 Ship Building of China 43 25(in Chinese)[纪 刚、张纬康 2002 中国造船 43 25]
[16] Lewis C P, Uar A, Bishop S R 1998 Transactions of the Institute of Measurement and Control 20 29
[17] Nbendjo B R N, Salissou Y, Woafo P 2005 Chaos, Solitons and Fractals 23 809
[18] Shang H L, Xu J 2009 Chaos, Solitons and Fractals 41 1880
[19] Soliman M S, Thompson J M T 1989 Journal of Sound and Vibration 35 453
[20] Shang H L, Xu J 2008 Journal of Tongji University (Natural Science) 36 962(in Chinese)[尚慧琳、徐 鉴 2008同济大学 学报 36 962] 〖23] Qian Q,Wang L, Ni Q 2008 Chin. Phys. B 17 569
[21] Zou S C, Xu W, Jin Y F 2008 Acta Phys. Sin. 57 7527(in Chinese) [邹少存、徐 伟、靳艳飞 2008 57 7527]
[22] Tatlier M, enatalar A E 2001 Chaos, Solitons and Fractals 12 1145
Catalog
Metrics
- Abstract views: 8693
- PDF Downloads: 862
- Cited By: 0
下载:
