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In this paper, Lorenz chaotic system with stochastic perturbation and unknown parameters is investigated, in which the stochastic perturbations is one-dimensional random process of the standard Wiener. Based on stochastic Lyapunov stability theory, It formula and adaptive control method combined with three adaptive control laws and two adaptive control laws respectively, two mean square Asymptotic adaptive synchronization standards are put forward theoretically. These new standards are in a simple form and easy to deal with. Moreover, with these standards, not only drive system with stochastic perturbations can be synchronized with the respond system, but also unknown parameters in the system can be identified. Finally, the Matlab numerical simulations confirm that the proposed results are correct and effective.
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Keywords:
- Lorenz chaotic system with stochastic perturbation /
- adaptive synchronization /
- stochastic Lyapunov stability theory /
- parameter identification
[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chen G R, L J H 2003 The Dynamics Analysis, Control and Synchronization of the Family of Lorenz System (Beijing: Science press) (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京:科学出版社) 第9页]
[3] Stwart I 2002 Nature 406 948
[4] Tucker W 1999 C R Acad Sci Paris 328 119
[5] Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. On Circuits & Systems-I 33 1072
[6] Chen G R, Ueta T 1999 Int. J. of Bifur Chaos 9 1465
[7] L J H, Chen G R 2002 Int. J. of Bifur Chaos 12 659
[8] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[9] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[10] Hu M, Yang Y, Xu Z 2008 Phys. Lett. A 372 3228
[11] Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun Nonlinear Sci Numer Simul. 14 1410
[12] Li G H 2005 Chin. Phys. 14 472
[13] Park J H, Ji D H, Won S C, Lee S M 2008 Applied Mathematics and Computation 204 170
[14] Hou Y Y, Liao T L, Yan J J 2007 Physica A 379 81
[15] Liu B, Shi P M, Liu S 2009 Acta Phys. Sin. 58 074383 (in Chinese) [刘彬, 时培明, 刘爽 2009 物理学报 58 074383]
[16] Zhao J C, Zhang Q J, Lu J A 2011 Chin. Phys. B 20 050507
[17] Lin J S, Yan J J 2009 Nonlinear Anal RWA 10 1151
[18] Li W L, Liu Z H, Miao J 2010 Commun Nonlinear Sci Numer Simulat 15 3015
[19] Wu X, Lu J 2003 Chaos, Solitons and Fractals 18 721
[20] Guo Z A, L L, Li Y, Xia X L 2007 Acta Phys. Sin. 56 95 (in Chinese) [郭治安, 吕翎, 李岩, 夏晓岚 2007 物理学报 56 95]
[21] Tu L L, Lu J A 2005 Chin. Phys. 14 1755
[22] Ma J, Su W T, Gao J Z 2010 Acta Phys. Sin. 59 1554 (in Chinese) [马军, 苏文涛, 高加振 2010 物理学报 59 1554]
[23] Tu L L, Ke C, Ding Y M 2011 Acta Phys. Sin. 60 056803 (in Chinese) [涂俐兰, 柯超, 丁咏梅 2011 物理学报 60 056803]
[24] Gong G L, Qian M P 2004 Application of Random process-and the random model in algorithm and intelligent computer (Beijing: Tsinghua University Press)
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Chen G R, L J H 2003 The Dynamics Analysis, Control and Synchronization of the Family of Lorenz System (Beijing: Science press) (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京:科学出版社) 第9页]
[3] Stwart I 2002 Nature 406 948
[4] Tucker W 1999 C R Acad Sci Paris 328 119
[5] Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. On Circuits & Systems-I 33 1072
[6] Chen G R, Ueta T 1999 Int. J. of Bifur Chaos 9 1465
[7] L J H, Chen G R 2002 Int. J. of Bifur Chaos 12 659
[8] Ott E, Grebogi C, Yorke J A 1990 Phys. Rev. Lett. 64 1196
[9] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[10] Hu M, Yang Y, Xu Z 2008 Phys. Lett. A 372 3228
[11] Wang H, Han Z Z, Xie Q Y, Zhang W 2009 Commun Nonlinear Sci Numer Simul. 14 1410
[12] Li G H 2005 Chin. Phys. 14 472
[13] Park J H, Ji D H, Won S C, Lee S M 2008 Applied Mathematics and Computation 204 170
[14] Hou Y Y, Liao T L, Yan J J 2007 Physica A 379 81
[15] Liu B, Shi P M, Liu S 2009 Acta Phys. Sin. 58 074383 (in Chinese) [刘彬, 时培明, 刘爽 2009 物理学报 58 074383]
[16] Zhao J C, Zhang Q J, Lu J A 2011 Chin. Phys. B 20 050507
[17] Lin J S, Yan J J 2009 Nonlinear Anal RWA 10 1151
[18] Li W L, Liu Z H, Miao J 2010 Commun Nonlinear Sci Numer Simulat 15 3015
[19] Wu X, Lu J 2003 Chaos, Solitons and Fractals 18 721
[20] Guo Z A, L L, Li Y, Xia X L 2007 Acta Phys. Sin. 56 95 (in Chinese) [郭治安, 吕翎, 李岩, 夏晓岚 2007 物理学报 56 95]
[21] Tu L L, Lu J A 2005 Chin. Phys. 14 1755
[22] Ma J, Su W T, Gao J Z 2010 Acta Phys. Sin. 59 1554 (in Chinese) [马军, 苏文涛, 高加振 2010 物理学报 59 1554]
[23] Tu L L, Ke C, Ding Y M 2011 Acta Phys. Sin. 60 056803 (in Chinese) [涂俐兰, 柯超, 丁咏梅 2011 物理学报 60 056803]
[24] Gong G L, Qian M P 2004 Application of Random process-and the random model in algorithm and intelligent computer (Beijing: Tsinghua University Press)
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