Nonlinear Local Lyapunov Exponent and Quantification of Local Predictability
DING Rui-Qiang1, LI Jian-Ping1, HA Kyung-Ja2
1State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 1000292Division of Earth Environmental System, Pusan National University, Busan 609-735, Korea
Nonlinear Local Lyapunov Exponent and Quantification of Local Predictability
DING Rui-Qiang1;LI Jian-Ping1;HA Kyung-Ja2
1State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 1000292Division of Earth Environmental System, Pusan National University, Busan 609-735, Korea
摘要Nonlinear local Lyapunov exponent (NLLE) is applied to quantitatively determine the local predictability limit of chaotic systems. As an example, we find that the local predictability limit of Henon attractor varies considerably with time, and some underlying phase-spatial structure does not appear. The local predictability limit of initially adjacent points in phase space may be completely different. This will cause difficulties in making the long-time analogue forecast.
Abstract：Nonlinear local Lyapunov exponent (NLLE) is applied to quantitatively determine the local predictability limit of chaotic systems. As an example, we find that the local predictability limit of Henon attractor varies considerably with time, and some underlying phase-spatial structure does not appear. The local predictability limit of initially adjacent points in phase space may be completely different. This will cause difficulties in making the long-time analogue forecast.
DING Rui-Qiang;LI Jian-Ping;HA Kyung-Ja. Nonlinear Local Lyapunov Exponent and Quantification of Local Predictability[J]. 中国物理快报, 2008, 25(5): 1919-1922.
DING Rui-Qiang, LI Jian-Ping, HA Kyung-Ja. Nonlinear Local Lyapunov Exponent and Quantification of Local Predictability. Chin. Phys. Lett., 2008, 25(5): 1919-1922.
[1] Eckmann J P and Ruelle D 1985 Rev. Mod. Phys. 57 617 [2] Oseledec V I 1968 Trans. Moscow Math. Soc. 19 197 [3] Lorenz E N 1965 Tellus 17 321 [4] Nese J M 1989 Physica D 35 237 [5] Mukougawa H et al %, Kimoto M and Yoden S1991 J. Atmos. Sci. 48 1231 [6] Kazantsev E 1999 Appl. Math. Comput. 104 217 [7] Ziemann C et al %, Smith L A and Kurths J2000 Phys. Lett. A 4237 [8] Yoden S and Nomura M 1993 J. Atmos. Sci. 50 1531 [9] Lacarra J F and Talagrand O 1988 Tellus A 40 81 [10] Mu M et al %, Duan W S and Wang B2003 Nonlinear Process.Geophys. 10 493 [11] Li J P, Ding R Q and Chen B H 2006 Review and Prospecton the Predictability Study of the Atmosphere (Beijing: ChinaMeteorology Press) p 96 [12] Ding R Q and Li J P 2007 Phys. Lett. A 364 396 [13] Chen B H et al %, Li J P and Ding R Q2006 Sci. Chin. D 49 1111 [14] Henon M 1976 Comm. Math. Phys. 50 69 [15] Bergen R E and Harnack R P 1982 Mon. Wea. Rev. 110 1083 [16] Toth Z 1989 J. Climat. 2 594 [17] Kalnay E and Dalcher A 1987 Mon. Wea. Rev. 115 349 [18] Legras B and Ghil M 1985 J. Atmos. Sci. 42 433
2008, Vol. 25 
