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In this paper, the local maximum of joint entroy was computed using the symbolic analysis method so as to determine the appropriate delay time of the phase space reconstruction. The numerical experiments for three typical chaotic systems show that the present method could reduce computation, increase the efficiency, and also could obtain the optimum delay time accurately and rapidly. And it could reconstruct the original phase space from the time series effectively. Thus it provides a fast and effective way to identify the chaotic signal.
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Keywords:
- phase space reconstruction /
- delay time /
- joint entroy /
- symbolic analysis
[1] Jiang W L, Zhang S Q, Wang Y Q 2005 Chaos and Wavelet Based Fault Information Diagnosis (Beijing: National Defence Industry Press) p46 (in Chinese) [姜万录, 张淑清, 王益群 2005 基于混沌和小波的故障信息诊断 (北京: 国防工业出版社) 第46页]
[2] Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[3] Zhang S Q, Zhao Y C, Jia J, Zhang L G, Shangguan H L 2010 Chin. Phys. B 19 060514
[4] Tian Y C 1997 Systems Engineering Theory and Practice 05 48 (in Chinese) [田玉楚 1997 系统工程理论与实践 05 48]
[5] Lu X Q, Cao B, Zeng M 2006 Chinese J. Comput Phys. 23 184
[6] Zhang J, Fan Y Y, Li H M, Sun H Y, Jia M 2011 Chinese J. Comput Phys. 28 469 (in Chinese) [张菁, 樊养余, 李慧敏, 孙恒义, 贾蒙 2011 计算物理 28 469]
[7] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 0550 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2005 54 0550]
[8] Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys. Sin. 59 1576 (in Chinese) [张淑清, 贾健, 高敏, 韩叙 2010 59 1576]
[9] Zhu X K, Jia Y H 2005 Journal of Geomatics 05 3 (in Chinese) [祝晓坤, 贾永红 2005 测绘信息与工程 05 3]
[10] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2004 53 2877]
[11] Lehrman M, Rechester A B 1997 Phys. Rev. Lett. 78 54
[12] Rechester A B and White R B 1991 Phys. Lett. A 158 51
[13] Zhang Y 2004 J. Xiangtan Min. Inst. 19 75 (in Chinese) [张雨 2004 湘潭矿业学院学报 19 75]
[14] Azad R K, Rao J S, Ramaswamy R 2002 Chao Solitons and Fractals 14 633
[15] Xiang K, Jiang J P 2007 PR&AI 20 154 (in Chinese) [向馗, 蒋静坪 2007 模式识别与人工智能 20 154]
[16] Shi Y S, Jiang Y, Song Y X 2011 Journal of Aerospace Power 26 670 (in Chinese) [史永胜, 姜颖, 宋云雪 2011 航空动力学报 26 670]
[17] Yu W B 2008 Calculate Experiment and Analysis on Chaos (Beijing: Science Press) p33 (in Chinese) [于万波 2008 混沌的计算实验与分析 (北京: 科学出版社) 第33页]
[18] Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamics (Beijing: Higher Education Press) p71 (in Chinese) [刘宗华 2006 混沌动力学基础及其应用 (北京: 高等教育出版社) 第71页]
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[1] Jiang W L, Zhang S Q, Wang Y Q 2005 Chaos and Wavelet Based Fault Information Diagnosis (Beijing: National Defence Industry Press) p46 (in Chinese) [姜万录, 张淑清, 王益群 2005 基于混沌和小波的故障信息诊断 (北京: 国防工业出版社) 第46页]
[2] Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[3] Zhang S Q, Zhao Y C, Jia J, Zhang L G, Shangguan H L 2010 Chin. Phys. B 19 060514
[4] Tian Y C 1997 Systems Engineering Theory and Practice 05 48 (in Chinese) [田玉楚 1997 系统工程理论与实践 05 48]
[5] Lu X Q, Cao B, Zeng M 2006 Chinese J. Comput Phys. 23 184
[6] Zhang J, Fan Y Y, Li H M, Sun H Y, Jia M 2011 Chinese J. Comput Phys. 28 469 (in Chinese) [张菁, 樊养余, 李慧敏, 孙恒义, 贾蒙 2011 计算物理 28 469]
[7] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 0550 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2005 54 0550]
[8] Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys. Sin. 59 1576 (in Chinese) [张淑清, 贾健, 高敏, 韩叙 2010 59 1576]
[9] Zhu X K, Jia Y H 2005 Journal of Geomatics 05 3 (in Chinese) [祝晓坤, 贾永红 2005 测绘信息与工程 05 3]
[10] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese) [肖方红, 阎桂荣, 韩宇航 2004 53 2877]
[11] Lehrman M, Rechester A B 1997 Phys. Rev. Lett. 78 54
[12] Rechester A B and White R B 1991 Phys. Lett. A 158 51
[13] Zhang Y 2004 J. Xiangtan Min. Inst. 19 75 (in Chinese) [张雨 2004 湘潭矿业学院学报 19 75]
[14] Azad R K, Rao J S, Ramaswamy R 2002 Chao Solitons and Fractals 14 633
[15] Xiang K, Jiang J P 2007 PR&AI 20 154 (in Chinese) [向馗, 蒋静坪 2007 模式识别与人工智能 20 154]
[16] Shi Y S, Jiang Y, Song Y X 2011 Journal of Aerospace Power 26 670 (in Chinese) [史永胜, 姜颖, 宋云雪 2011 航空动力学报 26 670]
[17] Yu W B 2008 Calculate Experiment and Analysis on Chaos (Beijing: Science Press) p33 (in Chinese) [于万波 2008 混沌的计算实验与分析 (北京: 科学出版社) 第33页]
[18] Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamics (Beijing: Higher Education Press) p71 (in Chinese) [刘宗华 2006 混沌动力学基础及其应用 (北京: 高等教育出版社) 第71页]
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