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In this paper a method is proposed to estimate the unknown parameters of nonlinear map based on the discrete variational principle, which can be applied to all map chaotic systems governed by the following equation: xk+1 = F(xk,). Numerical simulations on the well-known Logistic map and Henn map are conducted and all unknown parameters of the two discrete chaotic systems are identified respectively. Simulation results show that the discrete variational method is effective for parameter identification of the map chaotic system.
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Keywords:
- chaotic system /
- parameter identification /
- discrete variational method /
- adjoint equation
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Li G H 2005 Chaos. Soliton and Fractals. 32 1454
[3] Tu L L 2011 Chin. Phys. B 20 030504
[4] Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 100501
[5] Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[6] He M F, Mu Y M, Zhao L Z 2000 Acta Phys. Sin. 49 830 (in Chinese) [贺明峰, 穆云明, 赵立中 2000 49 830]
[7] Guan X P, Peng H P, Li L X, Wang X Q 2001 Acta Phys. Sin. 50 26 (in Chinese) [关新平, 彭海朋, 李丽香, 王益群 2001 50 26 ]
[8] Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤 勇 2002 51 2459]
[9] He Q, Wang L, Liu B 2007 Chaos. Soliton and Fractals. 34 654
[10] Li L X, Peng H P, Yang Y X, Wang X D 2007 Acta Phys. Sin. 56 51 (in Chinese) [李丽香, 彭海朋、, 杨义先, 王向东 2007 56 51]
[11] Li N Q, Pan W, Yan L S, Luo B 2011 Chin. Phys. B 20 060502
[12] Huang S X, Wu R S 2001 Mathematical Physics Problems in Atmosphere Science (Beijing: Meteorology Press) (in Chinese) [黄思训, 伍荣生 2001 大气科学中的数学物理问题(北京: 气象出版社)]
[13] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁, 黄娟娟 2006 55 3997]
[14] He J H 2008 Int. J. Modern. Phys. B 22 3487
[15] He J H 1997 Int. J. Turbo. Jet-Eng. 14 23
[16] He J H 2000 Appl. Math. Mech. 21 797
[17] He J H 2001 Int. J. Nonlin. Sci. Numer. 2 309
[18] He J H, Lee E W M 2009 Phys. Lett. A 373 1644
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Li G H 2005 Chaos. Soliton and Fractals. 32 1454
[3] Tu L L 2011 Chin. Phys. B 20 030504
[4] Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 100501
[5] Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[6] He M F, Mu Y M, Zhao L Z 2000 Acta Phys. Sin. 49 830 (in Chinese) [贺明峰, 穆云明, 赵立中 2000 49 830]
[7] Guan X P, Peng H P, Li L X, Wang X Q 2001 Acta Phys. Sin. 50 26 (in Chinese) [关新平, 彭海朋, 李丽香, 王益群 2001 50 26 ]
[8] Dai D, Ma X K, Li F C, You Y 2002 Acta Phys. Sin. 51 2459 (in Chinese) [戴栋, 马西奎, 李富才, 尤 勇 2002 51 2459]
[9] He Q, Wang L, Liu B 2007 Chaos. Soliton and Fractals. 34 654
[10] Li L X, Peng H P, Yang Y X, Wang X D 2007 Acta Phys. Sin. 56 51 (in Chinese) [李丽香, 彭海朋、, 杨义先, 王向东 2007 56 51]
[11] Li N Q, Pan W, Yan L S, Luo B 2011 Chin. Phys. B 20 060502
[12] Huang S X, Wu R S 2001 Mathematical Physics Problems in Atmosphere Science (Beijing: Meteorology Press) (in Chinese) [黄思训, 伍荣生 2001 大气科学中的数学物理问题(北京: 气象出版社)]
[13] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁, 黄娟娟 2006 55 3997]
[14] He J H 2008 Int. J. Modern. Phys. B 22 3487
[15] He J H 1997 Int. J. Turbo. Jet-Eng. 14 23
[16] He J H 2000 Appl. Math. Mech. 21 797
[17] He J H 2001 Int. J. Nonlin. Sci. Numer. 2 309
[18] He J H, Lee E W M 2009 Phys. Lett. A 373 1644
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