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A new circuit unit for the analysis and synthesis of the chaotic behaviors in the new fractional-order system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to demonstrate the dynamic behaviors of the fractional-order Liu system with α=09 An effective controller is designed based on a theory of stability identification based on Lyapunov equation. The results between simulation and experiment are in good agreement, thereby proving the existence of chaos in the fractional-order new system and the effectiveness of our proposed control method.
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Keywords:
- fractional-order chaotic system /
- circuit experiment /
- chaos control
[1] ［1]Hartly T T, Lorenzo C F， Qammer H K 1995 IEEE Trans. CAS-I 42 485
[2] ［2]Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[3] ［3]Li C P, Peng G J 2004 Chaos，Solitons and Fractals. 22 443
[4] ［4]Li C G, Chen G R 2004 Chaos, Solitions and Fractals 22 549
[5] ［5]Deng W H, Li C P 2005 Physica A 353 61
[6] ［6]Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 （in Chinese）［王发强、刘崇新 2006 55 3922］
[7] ［7]Lu J J, Liu C X 2007 Chin. Phys. 16 1586
[8] ［8]Xu Z, Liu C X 2008 Chin.Phys. B 17 4033
[9] ［9]Li C G, Chen G R 2004 Physica A 341 55
[10] ［10]Liu C X 2006 Far East J. Dynamical System 8 51
[11] ［11]Gao X, Yu J B 2005 Chin. Phys. 14 908
[12] ［12]Charef A, Sun H H, Tsao Y Y, Onaral B 1992 IEEE Trans. Auto. Contr. 37 9
[13] ［13]Liu C X，Liu T，Liu K，Liu L 2004 Chaos, Solitions and Fractals 22 1031
[14] ［14]Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[15] ［15]Zhao P D, Zhang X D 2008 Acta Phys. Sin. 57 2791 （in Chinese）［赵品栋、张晓丹 2008 57 2791］
[16] ［16]Matignon D 1996 In: IMACS, IEEE-SMC, Lille, France 963
[17] ［17]Hu J B, Han Y, Zhao L D. 2008 Acta Phys. Sin 57 7522 （in chinese）［胡建兵、韩焱、赵灵冬 2008 57 7522］
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[1] ［1]Hartly T T, Lorenzo C F， Qammer H K 1995 IEEE Trans. CAS-I 42 485
[2] ［2]Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[3] ［3]Li C P, Peng G J 2004 Chaos，Solitons and Fractals. 22 443
[4] ［4]Li C G, Chen G R 2004 Chaos, Solitions and Fractals 22 549
[5] ［5]Deng W H, Li C P 2005 Physica A 353 61
[6] ［6]Wang F Q, Liu C X 2006 Acta Phys. Sin. 55 3922 （in Chinese）［王发强、刘崇新 2006 55 3922］
[7] ［7]Lu J J, Liu C X 2007 Chin. Phys. 16 1586
[8] ［8]Xu Z, Liu C X 2008 Chin.Phys. B 17 4033
[9] ［9]Li C G, Chen G R 2004 Physica A 341 55
[10] ［10]Liu C X 2006 Far East J. Dynamical System 8 51
[11] ［11]Gao X, Yu J B 2005 Chin. Phys. 14 908
[12] ［12]Charef A, Sun H H, Tsao Y Y, Onaral B 1992 IEEE Trans. Auto. Contr. 37 9
[13] ［13]Liu C X，Liu T，Liu K，Liu L 2004 Chaos, Solitions and Fractals 22 1031
[14] ［14]Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[15] ［15]Zhao P D, Zhang X D 2008 Acta Phys. Sin. 57 2791 （in Chinese）［赵品栋、张晓丹 2008 57 2791］
[16] ［16]Matignon D 1996 In: IMACS, IEEE-SMC, Lille, France 963
[17] ［17]Hu J B, Han Y, Zhao L D. 2008 Acta Phys. Sin 57 7522 （in chinese）［胡建兵、韩焱、赵灵冬 2008 57 7522］
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