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Family of switched unified chaotic system

Liu Yang-Zheng Lin Chang-Sheng Li Xin-Chao

Family of switched unified chaotic system

Liu Yang-Zheng, Lin Chang-Sheng, Li Xin-Chao
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  • A nonlinear function of unified chaotic system, the family of switched unified chaotic system is generated which contains six kinds of subsystems. Each subsystem can be switched by changing systematic parameter values in parameter space, and these subsystems can be switched continuously from one to another via changing nonlinear function in state space. The features of these subsystems are analyzed in detail using Lyapunov exponent and bifurcation diagram. The division-time switching of unified chaotic system is realized based on digital signal processing (DSP).
    • Funds:
    [1]

    Li Y X, Chen G R, Wallace K S T 2005 IEEE Trans. Circuits Syst. Ⅱ 52 204

    [2]

    Wu X Q, Wang J J, Lu J A, Herbert H C I 2007 Chaos Soliton. Fract. 32 1485

    [3]

    Ge Z M,Yang K W 2007 Chaos Soliton. Fract. 33 246

    [4]

    Liu Y Z, Lin C S,Li X C,Liu H P,Wang Z L 2011 Acta Phys. Sin.60 030502 (in Chinese) [刘扬正、林长圣、李心朝、刘海鹏、王忠林 2011 物理学报 60 030502]

    [5]

    mer Morgül 2000 IEEE Trans. Circuits Syst. Ⅰ 47 1424

    [6]

    Lü J H, Chen G 2006 Int. J. Bifur. Chaos 16 775

    [7]

    Luo X H, Li H Q, Dai X G 2008 Acta Phys. Sin. 57 7511 (in Chinese) [罗小华、李华青、代祥光 2008物理学报 57 7511]

    [8]

    Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 57 3337 (in Chinese) [谌 龙、彭海军、王德石 2008 物理学报 57 3337]

    [9]

    Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 物理学报 54 1500]

    [10]

    Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞、禹思敏 2009 物理学报 58 120]

    [11]

    Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 物理学报 56 1983]

    [12]

    Zhang C X, Yu S M 2009 Chin. Phys. B 18 119

    [13]

    Elwakil A S, zguz S, Kennedy M P 2002 IEEE Trans. Circuits Syst. Ⅰ 49 527

    [14]

    Sprott J C 2000 Phys. Lett. A 266 19

    [15]

    Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707]

    [16]

    Lü J H, Yu X H, Chen G R 2003 IEEE Trans. Circuits Syst. Ⅰ 50 198

    [17]

    Chen Q F, Hong Y G, Chen G R, Zhong Q H, David J H 2006 IEEE Trans. Circuits Syst. Ⅰ 53 2692

    [18]

    Liu X Z, Teo K L, Zhang H T, Chen G R 2006 Chaos Soliton. Fract. 30 725

    [19]

    Guo J J, Xie G M, Wang L 2009 Chaos Soliton. Fract. 40 2160

    [20]

    Suzuki Takashi, Saito Toshimichi 1994 IEEE Trans. Circuits Syst. Ⅰ 41 876

    [21]

    Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 物理学报 58 8139]

    [22]

    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]

    [23]

    Wang G Y, He H L 2008 Chin. Phys. B 17 4014

    [24]

    Liu Y Z, Jiang C S, Lin C S, Sun H 2007 Acta Phys. Sin. 56 5131 (in Chinese) [刘扬正、姜长生、林长圣、孙 晗 2007 物理学报 56 5131]

    [25]

    Zhang Y J, Wang C P, Wang G Y, Xu N, Wang Z L 2009 J. China Unier. Posts Telecom. 16 122

    [26]

    Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun Nonlinear Sci. Numer Simulat 14 2239

    [27]

    Grzybowsk J M V, Rafikov M, Balthazar J M 2009 Commun Nonlinear Sci. Numer Simulat 14 2793

    [28]

    Danca M F, Wallace K S T, Chen G R 2008 Applied Mathematics and Computation 201 650

    [29]

    Lin C X, Hao J H 2008 J. Dyn. Contr. 6 254 (in Chinese) [林彩霞、郝建红 2008 动力学与控制学报 6 254]

    [30]

    Yu W W, Cao J D, Yuan K 2008 Phys. Lett. A 372 4438

    [31]

    Qi G Y, Chen G R,Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295

    [32]

    Liu C X,Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031

    [33]

    Wang G Y, Qiu S S, Xu Z Y 2006 Acta Phys. Sin. 55 3295 (in Chinese) [王光义、丘水生、许志益 2006 物理学报 55 3295]

    [34]

    Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872

    [35]

    Wang F Z, Chen Z Q, Wu W J,Yuan Z Z 2007 Chin. Phys. 16 3238

    [36]

    Cai G L,Tan Z H, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振海、周维怀、涂文桃 2007 物理学报 56 6230]

    [37]

    Liu Y Z, Lin C S, Wang Z L 2010 Acta Phys. Sin. 59 8407 (in Chinese) [刘扬正、林长圣、王忠林 2010 物理学报 59 8407]

  • [1]

    Li Y X, Chen G R, Wallace K S T 2005 IEEE Trans. Circuits Syst. Ⅱ 52 204

    [2]

    Wu X Q, Wang J J, Lu J A, Herbert H C I 2007 Chaos Soliton. Fract. 32 1485

    [3]

    Ge Z M,Yang K W 2007 Chaos Soliton. Fract. 33 246

    [4]

    Liu Y Z, Lin C S,Li X C,Liu H P,Wang Z L 2011 Acta Phys. Sin.60 030502 (in Chinese) [刘扬正、林长圣、李心朝、刘海鹏、王忠林 2011 物理学报 60 030502]

    [5]

    mer Morgül 2000 IEEE Trans. Circuits Syst. Ⅰ 47 1424

    [6]

    Lü J H, Chen G 2006 Int. J. Bifur. Chaos 16 775

    [7]

    Luo X H, Li H Q, Dai X G 2008 Acta Phys. Sin. 57 7511 (in Chinese) [罗小华、李华青、代祥光 2008物理学报 57 7511]

    [8]

    Chen L, Peng H J, Wang D S 2008 Acta Phys. Sin. 57 3337 (in Chinese) [谌 龙、彭海军、王德石 2008 物理学报 57 3337]

    [9]

    Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 物理学报 54 1500]

    [10]

    Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞、禹思敏 2009 物理学报 58 120]

    [11]

    Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强、刘崇新 2007 物理学报 56 1983]

    [12]

    Zhang C X, Yu S M 2009 Chin. Phys. B 18 119

    [13]

    Elwakil A S, zguz S, Kennedy M P 2002 IEEE Trans. Circuits Syst. Ⅰ 49 527

    [14]

    Sprott J C 2000 Phys. Lett. A 266 19

    [15]

    Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707]

    [16]

    Lü J H, Yu X H, Chen G R 2003 IEEE Trans. Circuits Syst. Ⅰ 50 198

    [17]

    Chen Q F, Hong Y G, Chen G R, Zhong Q H, David J H 2006 IEEE Trans. Circuits Syst. Ⅰ 53 2692

    [18]

    Liu X Z, Teo K L, Zhang H T, Chen G R 2006 Chaos Soliton. Fract. 30 725

    [19]

    Guo J J, Xie G M, Wang L 2009 Chaos Soliton. Fract. 40 2160

    [20]

    Suzuki Takashi, Saito Toshimichi 1994 IEEE Trans. Circuits Syst. Ⅰ 41 876

    [21]

    Hu G S 2009 Acta Phys. Sin. 58 8139 (in Chinese) [胡国四 2009 物理学报 58 8139]

    [22]

    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]

    [23]

    Wang G Y, He H L 2008 Chin. Phys. B 17 4014

    [24]

    Liu Y Z, Jiang C S, Lin C S, Sun H 2007 Acta Phys. Sin. 56 5131 (in Chinese) [刘扬正、姜长生、林长圣、孙 晗 2007 物理学报 56 5131]

    [25]

    Zhang Y J, Wang C P, Wang G Y, Xu N, Wang Z L 2009 J. China Unier. Posts Telecom. 16 122

    [26]

    Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun Nonlinear Sci. Numer Simulat 14 2239

    [27]

    Grzybowsk J M V, Rafikov M, Balthazar J M 2009 Commun Nonlinear Sci. Numer Simulat 14 2793

    [28]

    Danca M F, Wallace K S T, Chen G R 2008 Applied Mathematics and Computation 201 650

    [29]

    Lin C X, Hao J H 2008 J. Dyn. Contr. 6 254 (in Chinese) [林彩霞、郝建红 2008 动力学与控制学报 6 254]

    [30]

    Yu W W, Cao J D, Yuan K 2008 Phys. Lett. A 372 4438

    [31]

    Qi G Y, Chen G R,Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295

    [32]

    Liu C X,Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031

    [33]

    Wang G Y, Qiu S S, Xu Z Y 2006 Acta Phys. Sin. 55 3295 (in Chinese) [王光义、丘水生、许志益 2006 物理学报 55 3295]

    [34]

    Wang G Y, Qiu S S, Li H W, Li C F, Zheng Y 2006 Chin. Phys. 15 2872

    [35]

    Wang F Z, Chen Z Q, Wu W J,Yuan Z Z 2007 Chin. Phys. 16 3238

    [36]

    Cai G L,Tan Z H, Zhou W H, Tu W T 2007 Acta Phys. Sin. 56 6230 (in Chinese) [蔡国梁、谭振海、周维怀、涂文桃 2007 物理学报 56 6230]

    [37]

    Liu Y Z, Lin C S, Wang Z L 2010 Acta Phys. Sin. 59 8407 (in Chinese) [刘扬正、林长圣、王忠林 2010 物理学报 59 8407]

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  • Received Date:  11 June 2010
  • Accepted Date:  10 July 2010
  • Published Online:  15 April 2011

Family of switched unified chaotic system

  • 1. Institute of Nonlinear Physics, Nanjing Institute of Technology,Nanjing 211167,China

Abstract: A nonlinear function of unified chaotic system, the family of switched unified chaotic system is generated which contains six kinds of subsystems. Each subsystem can be switched by changing systematic parameter values in parameter space, and these subsystems can be switched continuously from one to another via changing nonlinear function in state space. The features of these subsystems are analyzed in detail using Lyapunov exponent and bifurcation diagram. The division-time switching of unified chaotic system is realized based on digital signal processing (DSP).

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