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Study on the mean absolute growth of model error for chaos system

Yang Jin-Hui Song Jun-Qiang

Study on the mean absolute growth of model error for chaos system

Yang Jin-Hui, Song Jun-Qiang
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  • Mean absolute growth of model error which is used to describe the initial error growth for chaos system, is employed in this paper to investigate the model error growth, and some meaningful conclusions are drew from it. It is found that the mean absolute growth of model error is initially exponential with a growth rate which has no direct relationship with the largest Lyapunov exponent. Afterwards model error growth enters into a nonlinear phase with a decreasing growth rate, and finally reaches a saturation value. If the difference between the attractor of real system and that of the model system is very small, the model error saturation level is consistent with the initial error saturation level of real system. With these conclusions one can obtain the predictability limit of a model easily, which is meaningful for weather prediction models. Also the predictability limit of model can be used for model comparison. The exacter model has a higher predictability limit which is useful for new model development.
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    Kantz H, Schreiber T 2004 Nonlinear Time Series Analysis, Cambridge University. Press, Cambridge

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    Orrell D 2005 J. Atmos. Sci. 62 1652

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    Nicolis C 2003 J. Atmos. Sci. 60 2208

    [12]

    Nicolis C 2004 J. Atmos. Sci. 61 1740

    [13]

    Ding R Q, Li J P 2008 Acta Phys. Sin. 57 7494 (in Chinese) [丁瑞强, 李建平 2008 物理学报 57 7494]

    [14]

    杨锦辉 宋君强 2012 物理学报 17 61

    [15]

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

    [16]

    Lorenz E N 1995 Proceedings of a Seminar Held at ECMWF on Predictability (Reading: ECMWF) p1

    [17]

    Orrell D 2003 J. Atmos. Sci. 60 2219

  • [1]

    Eckmann J P, Ruelle D 1985 Rev. Mod. Phys. 57 617

    [2]

    Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285

    [3]

    Sano M, Sawada Y 1985 Phys. Rev. Lett. 55 1082

    [4]

    Kantz H, Schreiber T 2004 Nonlinear Time Series Analysis, Cambridge University. Press, Cambridge

    [5]

    Ding R Q, Li J P 2007 Phys. Lett. A 364 396

    [6]

    Anderson J 2001 Mon. Wea. Rev. 129 2884

    [7]

    Whitaker J, T. Hamill 2002 Mon. Wea. Rev. 130 1913

    [8]

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

    [9]

    Orrell D, Smith L, Barkmeijer J 2001 Nonlinear Processes in Geophysics 8 357

    [10]

    Orrell D 2005 J. Atmos. Sci. 62 1652

    [11]

    Nicolis C 2003 J. Atmos. Sci. 60 2208

    [12]

    Nicolis C 2004 J. Atmos. Sci. 61 1740

    [13]

    Ding R Q, Li J P 2008 Acta Phys. Sin. 57 7494 (in Chinese) [丁瑞强, 李建平 2008 物理学报 57 7494]

    [14]

    杨锦辉 宋君强 2012 物理学报 17 61

    [15]

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

    [16]

    Lorenz E N 1995 Proceedings of a Seminar Held at ECMWF on Predictability (Reading: ECMWF) p1

    [17]

    Orrell D 2003 J. Atmos. Sci. 60 2219

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    [2] Yang Jin-Hui, Song Jun-Qiang. Saturation property of mean growth of initial error for chaos systems. Acta Physica Sinica, 2012, 61(17): 170511. doi: 10.7498/aps.61.170511
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    [4] Zhang Hua-Guang, Li Ai-Ping, Meng Zi-Yi, Yang Dong-Sheng. Generalized synchronization of two non-identical chaotic systems based on fuzzy model. Acta Physica Sinica, 2007, 56(6): 3121-3126. doi: 10.7498/aps.56.3121
    [5] Yu Ling-Hui, Liu Xiao-Jing, Gao Mei-Jing, Wu Shi-Chang, Lu Zhi-Gang. . Acta Physica Sinica, 2002, 51(10): 2211-2215. doi: 10.7498/aps.51.2211
    [6] Zhang Ling-Mei, Zhang Jian-Wen, Wu Run-Heng. Anti-control of Hopf bifurcation in the new chaotic system with piecewise system and exponential system. Acta Physica Sinica, 2014, 63(16): 160505. doi: 10.7498/aps.63.160505
    [7] Wang Jie-Zhi, Chen Zeng-Qiang, Yuan Zhu-Zhi. A new chaotic system and analysis of its properties. Acta Physica Sinica, 2006, 55(8): 3956-3963. doi: 10.7498/aps.55.3956
    [8] Luo Run-Zi. Impulsive control and synchronization of a new chaotic system. Acta Physica Sinica, 2007, 56(10): 5655-5660. doi: 10.7498/aps.56.5655
    [9] Zhang Jian-Xiong, Tang Wan-Sheng, Xu Yong. A new three-dimensional chaotic system. Acta Physica Sinica, 2008, 57(11): 6799-6807. doi: 10.7498/aps.57.6799
    [10] Song Yun-Zhong, Li Wen-Lin. Chaos anti-control of nonlinear system with uncertainties. Acta Physica Sinica, 2008, 57(1): 51-55. doi: 10.7498/aps.57.51
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  • Received Date:  18 April 2012
  • Accepted Date:  10 June 2012
  • Published Online:  20 November 2012

Study on the mean absolute growth of model error for chaos system

  • 1. School of computer, National University of Defense Technology, Changsha 410073, China

Abstract: Mean absolute growth of model error which is used to describe the initial error growth for chaos system, is employed in this paper to investigate the model error growth, and some meaningful conclusions are drew from it. It is found that the mean absolute growth of model error is initially exponential with a growth rate which has no direct relationship with the largest Lyapunov exponent. Afterwards model error growth enters into a nonlinear phase with a decreasing growth rate, and finally reaches a saturation value. If the difference between the attractor of real system and that of the model system is very small, the model error saturation level is consistent with the initial error saturation level of real system. With these conclusions one can obtain the predictability limit of a model easily, which is meaningful for weather prediction models. Also the predictability limit of model can be used for model comparison. The exacter model has a higher predictability limit which is useful for new model development.

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