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This paper proposes a method of information entropy optimized parameters (IEOP) of pahse space recon struction. First, it establishes an information entropy optimum model in phase space for embedding dimension and delay time by using conditional entropy. It then solves these two parameters with genetic algorithm (GA) simultaneously. IEOP constructs an optimum phase space, which maintains independence of reconstruction coordinate and retains the dynamic characteristics of the original system. In the numerical simulations, results of the Lorenz system and Mackey-Glass system show that it not only determines two parameters at the same time, but also can obtains more information in the optimized phase space, there by improving the performance of chaotic time series prediction.
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Keywords:
- information entropy /
- optimized parameters /
- chaotic time series /
- prediction
[1] Yan H, Wei P, Xiao X C 2009 Chin. Phys. B 18 3287
[2] Ma Q L, Zheng Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese)[马千里、郑启伦、 彭 宏、 覃姜维 2009 58 1410]
[3] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[4] Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713 (in Chinese)[张军峰、 胡寿松 2007 56 713]
[5] Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120 (in Chinese)[王永生、 孙 瑾、 王昌金、范洪达 2008 57 6120]
[6] Peng S G, Yu S M 2009 Chin. Phys. B 18 3758
[7] Wang D F, Han P 2008 Chin. Phys. B 17 3603
[8] Hu Y X, Gao J F 2005 Acta Phys. Sin. 54 5034 (in Chinese) [胡玉霞、 高金峰 2005 54 5034]
[9] Liu F C, Zhang Y L, Chen C 2008 Acta Phys. Sin. 57 2784 (in Chinese)[刘福才、 张彦柳、 陈 超 2008 57 2784]
[10] Han M, Shi Z W, Guo W 2007 Acta Phys. Sin. 56 43 (in Chinese)[韩 敏、 史志伟、 郭 伟 2007 56 43]
[11] Takens F 1981 Dynamical Systems and Turbulence (Berlin: SpringVerlag) 366
[12] Albano A M 1988 Phys. Rev. A 38 3017
[13] Fraser A M 1989 IEEE Trans. on Information Theory 35 245
[14] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese)[肖方红、阎桂荣、 韩宇航 2005 54 550]
[15] Yang S Q, Jia C Y 2002 Acta Phys. Sin. 51 2452 (in Chinese)[杨绍清、 贾传荧 2002 51 2452]
[16] Grassberg P, Procaccia I 1984 Physica 13 34
[17] Lu W, Wang H Y, Yao Z A, Li L 2009 Computer Science 36 187 (in Chinese)[吕 威、 王和勇、 姚正安、 李 磊 2009 计算机科学 36 187]
[18] Kugiumtzis D 1996 Physica D 95 13
[19] Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[20] Ataei M, Lohmann B, Khaki-Sedigh A, Lucas C 2004 Chaos, Solitons and Fractals 19 1131
[21] Tian Y C, Fu X T, Lu Y Z 1993 Control and Decision 8 345 (in Chinese)[田玉楚、 符雪桐、 吕勇哉 1993 控制与决策 8 345]
[22] Tian Y C 1997 Acta Phys. Sin. 46 442 (in Chinese) [田玉楚 1997 46 442]
[23] Elman J L 1990 Cognitive Science 14 179
[24] Mao J Q, Yao J, Ding H S 2009 Acta Phys. Sin. 58 2220 (in Chinese)[毛剑琴、 姚 健、丁海山 2009 58 2220]
[25] Jang J S R 1993 IEEE Trans. Syst. Man. 23 665
[26] He T, Zhou Z O 2007 Acta Phys. Sin. 56 693 (in Chinese)[贺 涛、 周正欧 2007 56 693]
[27] Zhang J S, Li H C, Xiao X C 2005 Chin. Phys. 14 49
[28] Ye M Y,Wang X D 2004 Chin. Phys. 13 454
[29] Aizenberg I, Moraga C 2007 Soft Comput. 11 169
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[1] Yan H, Wei P, Xiao X C 2009 Chin. Phys. B 18 3287
[2] Ma Q L, Zheng Q L, Peng H, Qin J W 2009 Acta Phys. Sin. 58 1410 (in Chinese)[马千里、郑启伦、 彭 宏、 覃姜维 2009 58 1410]
[3] Ma Q L, Zheng Q L, Peng H, Zhong T W, Qin J W 2008 Chin. Phys. B 17 536
[4] Zhang J F, Hu S S 2007 Acta Phys. Sin. 56 713 (in Chinese)[张军峰、 胡寿松 2007 56 713]
[5] Wang Y S, Sun J, Wang C J, Fan H D 2008 Acta Phys. Sin. 57 6120 (in Chinese)[王永生、 孙 瑾、 王昌金、范洪达 2008 57 6120]
[6] Peng S G, Yu S M 2009 Chin. Phys. B 18 3758
[7] Wang D F, Han P 2008 Chin. Phys. B 17 3603
[8] Hu Y X, Gao J F 2005 Acta Phys. Sin. 54 5034 (in Chinese) [胡玉霞、 高金峰 2005 54 5034]
[9] Liu F C, Zhang Y L, Chen C 2008 Acta Phys. Sin. 57 2784 (in Chinese)[刘福才、 张彦柳、 陈 超 2008 57 2784]
[10] Han M, Shi Z W, Guo W 2007 Acta Phys. Sin. 56 43 (in Chinese)[韩 敏、 史志伟、 郭 伟 2007 56 43]
[11] Takens F 1981 Dynamical Systems and Turbulence (Berlin: SpringVerlag) 366
[12] Albano A M 1988 Phys. Rev. A 38 3017
[13] Fraser A M 1989 IEEE Trans. on Information Theory 35 245
[14] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese)[肖方红、阎桂荣、 韩宇航 2005 54 550]
[15] Yang S Q, Jia C Y 2002 Acta Phys. Sin. 51 2452 (in Chinese)[杨绍清、 贾传荧 2002 51 2452]
[16] Grassberg P, Procaccia I 1984 Physica 13 34
[17] Lu W, Wang H Y, Yao Z A, Li L 2009 Computer Science 36 187 (in Chinese)[吕 威、 王和勇、 姚正安、 李 磊 2009 计算机科学 36 187]
[18] Kugiumtzis D 1996 Physica D 95 13
[19] Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[20] Ataei M, Lohmann B, Khaki-Sedigh A, Lucas C 2004 Chaos, Solitons and Fractals 19 1131
[21] Tian Y C, Fu X T, Lu Y Z 1993 Control and Decision 8 345 (in Chinese)[田玉楚、 符雪桐、 吕勇哉 1993 控制与决策 8 345]
[22] Tian Y C 1997 Acta Phys. Sin. 46 442 (in Chinese) [田玉楚 1997 46 442]
[23] Elman J L 1990 Cognitive Science 14 179
[24] Mao J Q, Yao J, Ding H S 2009 Acta Phys. Sin. 58 2220 (in Chinese)[毛剑琴、 姚 健、丁海山 2009 58 2220]
[25] Jang J S R 1993 IEEE Trans. Syst. Man. 23 665
[26] He T, Zhou Z O 2007 Acta Phys. Sin. 56 693 (in Chinese)[贺 涛、 周正欧 2007 56 693]
[27] Zhang J S, Li H C, Xiao X C 2005 Chin. Phys. 14 49
[28] Ye M Y,Wang X D 2004 Chin. Phys. 13 454
[29] Aizenberg I, Moraga C 2007 Soft Comput. 11 169
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