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A new method is proposed for the stabilization of spatio temporal chaos in a thyristor device. The valid control of unstable periodic orbits (UPOs) of the chaotic system is achieved by combining time-delayed feedback control (TDFC) with the use of phase space compression. Based on the stability theory of linear periodic system,the linear stability analysis of the controlled system is discussed by using the Floquets theorem,and the feedback gain of TDFC was optimized through the Floquet exponents. The results show that the spatio temporally unstable periodic orbits embedded in a chaotic attractor of the spatially extended system can be stabilized by using the proposed method,and the spiking current filaments can also be inhibited well.
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Keywords:
- thyristor /
- chaos /
- time-delayed feedback control /
- phase space compression
[1] Deane J H,Hamill D C 1990 IEEE Trans. Power Electron. 5 260
[2] Wacker A,Schll E 1994 Semicond. Sci. Tech. 9 592
[3] Ott E,Grebogi C,York J A 1990 Phys. Rev. Lett. 64 1196
[4] 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 3279]
[5] Gao J H,Xie L L,Peng J H 2009 Acta Phys. Sin. 58 5218 (in Chinese) [高继华、谢玲玲、彭建华 2009 物理学报 58 5218]
[6] Zhang X M,Peng J H,Chen G R 2004 Acta Phys. Sin. 53 2864 (in Chinese) [张晓明、彭建华、陈关荣 2004 物理学报 53 2864]
[7] Yan S L 2008 Acta Phys. Sin. 57 6878 (in Chinese) [颜森林 2008 物理学报 57 6878]
[8] Yang R,Zhang B 2007 Acta Phys. Sin. 56 3789 (in Chinese) [杨 汝、张 波 2007 物理学报 56 3789]
[9] Zhao Y B,Luo X S 2007 Acta Phys. Sin. 56 6258 (in Chinese) [赵益波、罗晓曙 2007 物理学报 56 6258]
[10] Pyragas K 1992 Phys. Lett. A 170 421
[11] Socolar J E S,Sukow D W,Gauthier D J 1994 Phys. Rev. E 50 3245
[12] Just W,Bernard T,Ostheirer M,Reibold E,Benner H 1997 Phys. Rev. Lett. 78 203
[13] Luo X S 1999 Acta Phys. Sin. 48 402 (in Chinese) [罗晓曙 1999 物理学报 48 402]
[14] Zhang X,Shen K 2001 Acta Phys. Sin. 50 624 (in Chinese) [张 旭、沈 柯 2001 物理学报 50 624]
[15] Jing X D,Lü L 2008 Acta Phys. Sin. 57 4766 (in Chinese) [敬晓丹、吕 翎 2008 物理学报 57 4766]
[16] Kehrt M,Hvel P,Flunkert V,Dahlem M A,Rodin P,Schll E 2009 Eur. Phys. J. B 68 557
[17] Unkelbach J,Amann A,Just W,Schll E 2003 Phys. Rev. E 68 026204
[18] Beck O,Amann A,Schll E,Socolar J E,Just W 2002 Phys. Rev. E 66 016213
[19] Pyragas K 2006 Philos. T. R. Soc. A 364 2309
[20] Tan P A,Zhang B,Qiu D Y 2010 Acta Phys. Sin. 59 3747(in Chinese) [谭平安、张 波、丘东元 2010 物理学报 59 3747]
[21] Dahms T,Hvel P,Schll E 2007 Phys. Rev. E 76 056201
[22] Agarwal R,Bohner M,Domoshnitsky A,Goltser Y 2005 Acta Math. Hung. 109 305
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[1] Deane J H,Hamill D C 1990 IEEE Trans. Power Electron. 5 260
[2] Wacker A,Schll E 1994 Semicond. Sci. Tech. 9 592
[3] Ott E,Grebogi C,York J A 1990 Phys. Rev. Lett. 64 1196
[4] 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 3279]
[5] Gao J H,Xie L L,Peng J H 2009 Acta Phys. Sin. 58 5218 (in Chinese) [高继华、谢玲玲、彭建华 2009 物理学报 58 5218]
[6] Zhang X M,Peng J H,Chen G R 2004 Acta Phys. Sin. 53 2864 (in Chinese) [张晓明、彭建华、陈关荣 2004 物理学报 53 2864]
[7] Yan S L 2008 Acta Phys. Sin. 57 6878 (in Chinese) [颜森林 2008 物理学报 57 6878]
[8] Yang R,Zhang B 2007 Acta Phys. Sin. 56 3789 (in Chinese) [杨 汝、张 波 2007 物理学报 56 3789]
[9] Zhao Y B,Luo X S 2007 Acta Phys. Sin. 56 6258 (in Chinese) [赵益波、罗晓曙 2007 物理学报 56 6258]
[10] Pyragas K 1992 Phys. Lett. A 170 421
[11] Socolar J E S,Sukow D W,Gauthier D J 1994 Phys. Rev. E 50 3245
[12] Just W,Bernard T,Ostheirer M,Reibold E,Benner H 1997 Phys. Rev. Lett. 78 203
[13] Luo X S 1999 Acta Phys. Sin. 48 402 (in Chinese) [罗晓曙 1999 物理学报 48 402]
[14] Zhang X,Shen K 2001 Acta Phys. Sin. 50 624 (in Chinese) [张 旭、沈 柯 2001 物理学报 50 624]
[15] Jing X D,Lü L 2008 Acta Phys. Sin. 57 4766 (in Chinese) [敬晓丹、吕 翎 2008 物理学报 57 4766]
[16] Kehrt M,Hvel P,Flunkert V,Dahlem M A,Rodin P,Schll E 2009 Eur. Phys. J. B 68 557
[17] Unkelbach J,Amann A,Just W,Schll E 2003 Phys. Rev. E 68 026204
[18] Beck O,Amann A,Schll E,Socolar J E,Just W 2002 Phys. Rev. E 66 016213
[19] Pyragas K 2006 Philos. T. R. Soc. A 364 2309
[20] Tan P A,Zhang B,Qiu D Y 2010 Acta Phys. Sin. 59 3747(in Chinese) [谭平安、张 波、丘东元 2010 物理学报 59 3747]
[21] Dahms T,Hvel P,Schll E 2007 Phys. Rev. E 76 056201
[22] Agarwal R,Bohner M,Domoshnitsky A,Goltser Y 2005 Acta Math. Hung. 109 305
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