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A new smooth quadratic chaotic system and its digital signal processing implementation

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

A new smooth quadratic chaotic system and its digital signal processing implementation

Liu Yang-Zheng, Lin Chang-Sheng, Li Xin-Chao
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  • Developing and changing nonlinear function of Lorenz chaotic system, a new autonomous chaotic system is generated which contains three smooth quadratic terms of system variables and five equilibriums. The characteristics of five equilibriums are discussed and a fractal dimension is calculated. The features of chaotic system are analyzed in detail using bifurcation diagram and Lyapunov exponent. The period doubling bifurcation of the system can occus. The chaotic system is realized based on digital signal processing. Experimental result shows the effectiveness and feasibility of the theoretical analysis and verifies the behaviors of various attractors.
    • Funds:
    [1]

    Lorenz E N 1963 J. Atmos. Sci. 20 130

    [2]

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

    [3]

    Miranda R, Stone E 1993 Phys. Lett. A 178 105

    [4]

    Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261

    [5]

    Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465

    [6]

    Lü J H, Chen G 2002 Int. J. Bifur. Chaos 12 659

    [7]

    Lü J H, Chen G, Cheng D 2004 Int. J. Bifur. Chaos 14 1507

    [8]

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

    [9]

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

    [10]

    Liu L, Su Y C, Liu C X 2007 Chin. Phys. 16 1897

    [11]

    Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍、 齐国元、 陈 增强、 张宇辉、 袁著祉 2006 物理学报 55 4005] 〖12] 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]

    [12]

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

    [13]

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

    [14]

    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]

    [15]

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

    [16]

    Shilnikov L P 1994 Int. J. Bifur. Chaos 4 489

    [17]

    Long M, Qiu S S 2007 Chin. Phys. 16 2254

  • [1]

    Lorenz E N 1963 J. Atmos. Sci. 20 130

    [2]

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

    [3]

    Miranda R, Stone E 1993 Phys. Lett. A 178 105

    [4]

    Liu W B, Chen G R 2003 Int. J. Bifur. Chaos 13 261

    [5]

    Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465

    [6]

    Lü J H, Chen G 2002 Int. J. Bifur. Chaos 12 659

    [7]

    Lü J H, Chen G, Cheng D 2004 Int. J. Bifur. Chaos 14 1507

    [8]

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

    [9]

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

    [10]

    Liu L, Su Y C, Liu C X 2007 Chin. Phys. 16 1897

    [11]

    Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍、 齐国元、 陈 增强、 张宇辉、 袁著祉 2006 物理学报 55 4005] 〖12] 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]

    [12]

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

    [13]

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

    [14]

    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]

    [15]

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

    [16]

    Shilnikov L P 1994 Int. J. Bifur. Chaos 4 489

    [17]

    Long M, Qiu S S 2007 Chin. Phys. 16 2254

  • [1] Lan Kang, Du Qian, Kang Li-Sha, Jiang Lu-Jing, Lin Zhen-Yu, Zhang Yan-Hui. The electron transfer properties of an open double quantum dot based on a quantum point contact. Acta Physica Sinica, 2020, 69(4): 1-11. doi: 10.7498/aps.69.20191718
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  • Received Date:  20 August 2010
  • Accepted Date:  16 September 2010
  • Published Online:  15 June 2011

A new smooth quadratic chaotic system and its digital signal processing implementation

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

Abstract: Developing and changing nonlinear function of Lorenz chaotic system, a new autonomous chaotic system is generated which contains three smooth quadratic terms of system variables and five equilibriums. The characteristics of five equilibriums are discussed and a fractal dimension is calculated. The features of chaotic system are analyzed in detail using bifurcation diagram and Lyapunov exponent. The period doubling bifurcation of the system can occus. The chaotic system is realized based on digital signal processing. Experimental result shows the effectiveness and feasibility of the theoretical analysis and verifies the behaviors of various attractors.

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