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The aim of this paper is to study a chaotic oscillators stability and chaos behavior and to determine the conditions for the stability and chaotic behavior of the chaotic oscillator by theoretical analysis. Furthermore,this study also aims to control the chaotic oscillator by an exact feedback linearization method. Finally,both numerical simulations and circuit experiments verify the validity of the theoretical analysis.
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Keywords:
- chaotic oscillator /
- stable condition /
- chaos /
- feedback control
[1] Lorenz E N 1963 J. Atmosph. Sci. 20 130
[2] Chua L O,Komuro M,Matsumoto T 1986 IEEE Trans. Circuits Syst. I 33 974
[3] Sprott J C 1994 Phys. Rev. E 50 647
[4] Chen G R,Ueta T 1999 Bifurcation and Chaos 9 1465
[5] Lü J H,Chen G R 2002 Bifurcation and Chaos 12 659
[6] Pecora L M,Carroll T L 1990 Phys. Rev. Lett. 64 821
[7] Guan X P,He Y H,Fan Z P 2003 Acta Phys. Sin. 52 276 (in Chinese) [关新平、何宴辉、范正平 2003 物理学报 52 276]
[8] Wang X Y,Meng J 2009 Acta Phys. Sin. 58 3780 (in Chinese) [王兴元、孟 娟 2009 物理学报 58 3780]
[9] Wei D Q,Luo X S,Qin Y H 2009 Chin. Phys. B 18 2184
[10] Zhang R X,Yang S P 2009 Chin. Phys. B 18 3295
[11] Zhou P,Cao Y X,Cheng X F 2009 Chin. Phys. B 18 1394
[12] Zhang Q J,Lu J A 2008 Chin. Phys. B 17 492
[13] Liu Y Z,Jiang C S 2009 Acta Phys. Sin. 58 771 (in Chinese) [刘扬正、姜长生 2009 物理学报 58 771]
[14] Gu Q L,Gao T G 2009 Chin. Phys. B 18 84
[15] Yu S M 2008 Acta Phys. Sin. 57 3374 (in Chinese) [禹思敏 2008 物理学报 57 3374]
[16] Yu S M,Lü J H,Chen G R 2007 IEEE Trans. Circuits Syst. I 54 2087
[17] Matouk A E,Agiza H N 2008 J. Math. Anal. Appl. 341 259
[18] Tamaevi Acˇ ius A,Namajūnas A,Cenys A 1996 Electronics Letters 32 957
[19] Lü J H,Lu J A,Chen S H 2002 Chaotic Time Series Analysis and Its Application (Wuhan:Wuhan University Press) p82 (in Chinese) [吕金虎、陆君安、陈士华 2002 混沌时间序列分析及其应用(武汉:武汉大学出版社)第82页]
[20] Jiang P Q,Luo X S,Wang B H,Fang J Q,Chen G R,Zou Y L 2002 Acta Phys. Sin. 51 1937 (in Chinese) [蒋品群、罗晓曙、汪秉宏、方锦清、陈关荣、邹艳丽 2002 物理学报 51 1937]
[21] Khalil H K 1996 Nonlinear Systems (Boston:Prentice Hall Press) p522
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[1] Lorenz E N 1963 J. Atmosph. Sci. 20 130
[2] Chua L O,Komuro M,Matsumoto T 1986 IEEE Trans. Circuits Syst. I 33 974
[3] Sprott J C 1994 Phys. Rev. E 50 647
[4] Chen G R,Ueta T 1999 Bifurcation and Chaos 9 1465
[5] Lü J H,Chen G R 2002 Bifurcation and Chaos 12 659
[6] Pecora L M,Carroll T L 1990 Phys. Rev. Lett. 64 821
[7] Guan X P,He Y H,Fan Z P 2003 Acta Phys. Sin. 52 276 (in Chinese) [关新平、何宴辉、范正平 2003 物理学报 52 276]
[8] Wang X Y,Meng J 2009 Acta Phys. Sin. 58 3780 (in Chinese) [王兴元、孟 娟 2009 物理学报 58 3780]
[9] Wei D Q,Luo X S,Qin Y H 2009 Chin. Phys. B 18 2184
[10] Zhang R X,Yang S P 2009 Chin. Phys. B 18 3295
[11] Zhou P,Cao Y X,Cheng X F 2009 Chin. Phys. B 18 1394
[12] Zhang Q J,Lu J A 2008 Chin. Phys. B 17 492
[13] Liu Y Z,Jiang C S 2009 Acta Phys. Sin. 58 771 (in Chinese) [刘扬正、姜长生 2009 物理学报 58 771]
[14] Gu Q L,Gao T G 2009 Chin. Phys. B 18 84
[15] Yu S M 2008 Acta Phys. Sin. 57 3374 (in Chinese) [禹思敏 2008 物理学报 57 3374]
[16] Yu S M,Lü J H,Chen G R 2007 IEEE Trans. Circuits Syst. I 54 2087
[17] Matouk A E,Agiza H N 2008 J. Math. Anal. Appl. 341 259
[18] Tamaevi Acˇ ius A,Namajūnas A,Cenys A 1996 Electronics Letters 32 957
[19] Lü J H,Lu J A,Chen S H 2002 Chaotic Time Series Analysis and Its Application (Wuhan:Wuhan University Press) p82 (in Chinese) [吕金虎、陆君安、陈士华 2002 混沌时间序列分析及其应用(武汉:武汉大学出版社)第82页]
[20] Jiang P Q,Luo X S,Wang B H,Fang J Q,Chen G R,Zou Y L 2002 Acta Phys. Sin. 51 1937 (in Chinese) [蒋品群、罗晓曙、汪秉宏、方锦清、陈关荣、邹艳丽 2002 物理学报 51 1937]
[21] Khalil H K 1996 Nonlinear Systems (Boston:Prentice Hall Press) p522
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