非线性动力学方法在气候突变检测中的应用

刘群群; 何文平; 顾斌

doi:10.7498/aps.64.179201

摘要

快速、准确的检测气候突变, 对于我们认识气候系统的变化和对未来气候系统演变趋势的预测有着重要的现实意义和社会经济价值. 本文主要回顾了近年来非线性突变检测技术的主要研究进展及其在实际观测资料中的应用, 其中包括基于气候系统长程相关性的检测方法, 如滑动去趋势波动分析方法、滑动移除去趋势波动分析方法、滑动移除重标极差方法和指纹法等; 以及基于时间序列复杂性的检测方法, 如近似熵方法, Fisher信息和小波Fisher信息等. 此外, 本文还指出发展针对空间场的突变检测技术是未来一个可能的发展方向. 由于空间场所包含的气候系统的演变信息远高于单点时间序列, 空间场的突变检测技术将会使得对气候突变的检测时间大大缩短, 从而使得人们有足够的时间去采取行动, 以便为适应气候突变所带来的新挑战做好准备.

关键词:

Abstract

The research of abrupt climate change is an important field in the climate change. The rapid and accurate detection of the abrupt climate change has important practical significance and major economic-social costs, which will help us understand climate change and forecast the future evolutionary trend of the climate system. The detection results of most traditional abrupt climate change depend on the selection of the time scale concerned, which may result in the fact that we cannot identify an abrupt climate change until the event has been past for a long time. Moreover, these detection methods cannot extract the dynamical changes from the observational data of the climate system. As the rapid development in nonlinear science, the abrupt climate change detection technology has also been improved gradually. This article briefly reviews several new progresses in abrupt dynamical detection methods developed on the basis of recent nonlinear technologies, and some applications in the real observational data. These new methods mainly contain the technologies based on the long-range correlation of climate systems, such as moving detrended fluctuation analysis, moving cut data-detrended fluctuation analysis, moving cut data-R/S analysis, degenerate fingerprinting, and red noise. Moreover, some abrupt dynamical detection methods developed by the complexity of the time series, namely, entropy, such as approximate entropy, moving cutting data-approximate entropy, Fisher information, and wavelet Fisher's information measure. Furthermore, there are some other abrupt dynamical detection methods based on the theory of phase space, such as the dynamics exponent Q. Climate system is a complex dynamical system with nonlinear and interactive nature, which has long-range persistence in spatio-temporal variation, thus the abrupt detection method on spatial field change is pointed out to be a promising direction for further research in future. Because the spatial field contains abundance of information about the evolution of climate system which is much more than that in a time series in single meteorological station, the detecting methods on spatial field will greatly help us detect an abrupt climate change as soon as possible. And then we will have enough time to take action and make preparations for the new challenges due to the abrupt climate change.

Keywords:

作者及机构信息

1.
南京信息工程大学, 物理系, 南京 210044;

2.
南京信息工程大学, 空间天气研究所, 南京 210044;

3.
国家气候中心, 北京 100081;

4.
南京信息工程大学, 中国气象局气溶胶与云降水重点开放实验室, 南京 210044

通信作者: 何文平, wenping_he@163.com

基金项目: 全球变化研究国家重大科学研究计划(批准号: 2012CB955902)、国家自然科学基金(批准号: 41275074和41175067)、中国气象局气溶胶与云降水重点开放实验室开放课题(批准号: KDW1304)资助的课题.

Authors and contacts

1.
College of Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China;

2.
Institute of Space Weather, Nanjing University of Information Science and Technology, Nanjing 210044, China;

3.
National Climate Center, China Meteorological Administration, Beijing 100081, China;

4.
The Key Laboratory for Aerosol-Cloud-Precipitation of CMA-NUIST, Nanjing 210044, China

Corresponding author: He Wen-Ping, wenping_he@163.com

Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB955902), the National Natural Science Foundation of China (Grant Nos. 41275074, 41175067), the Program of the Key Laboratory for Aerosol-Cloud-Precipitation of CMA-NUIST (Grant No. KDW1304).

参考文献

[1]	Liu S D, Liu S K 1997 Chin. Sci. Bull. 42 1565 (in Chinese) [刘式达, 刘式适 1997 科学通报 42 1565]
[2]	Liu S D, Liu S K, Liang S, Ren K, Fu Z T 2002 Prog. Nat. Sci. 12 1 (in Chinese) [刘式达, 刘式适, 梁爽, 任奎, 付遵涛 2002 自然科学进展 12 1]
[3]	Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta. Phys. Sin 58 2853 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2009 58 2853]
[4]	Fu C B, Wang Q 1992 Chinese J. Atmos. Sci. 16 483 (in Chinese) [符淙斌, 王强 1992 大气科学 16 483]
[5]	Feng G L, Dong W J 2003 Chin. Phys. 12 1072
[6]	Feng G L, Dong W J, Li J P 2004 Chin. Phys. 13 1582
[7]	Li J P, Chou J F, Shi J E 1996 Journal of Beijing Meteorological college 2 16 (in Chinese) [李建平, 丑纪范, 史久恩 1996 北京气象学院 2 16]
[8]	Li J P, Shi J E 1993 Chinese J. Atmos. Sci. 17 132 (in Chinese) [李建平, 史久恩 1993 大气科学 17 132]
[9]	Xiao D, Li J P 2007 J. Geophys. Res. 112 D24S22
[10]	Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear theories and methods on spatial-temporal distribution of the obserbational data (Beijing: Metrological press) p27-89 [封国林, 董文杰, 龚志强, 侯威, 万仕全, 支蓉 2006 观测数据非线性时空分布理论和方法 (北京: 气象出版社)第 27–第89页]
[11]	Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[12]	Kendall M G 1970 Rank Correlation Methods (London: Charles Griffin)
[13]	Mann H B, Whitney D R 1947 Annals of Mathematical Statistics 18 50
[14]	Lepage 1971 Biometrika 58 213
[15]	He W P, Wan S Q, Jiang Y D, Jin H M, Zhang W, Wu Q, He T 2013 Int. J. Climatol. 33 2713
[16]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601
[17]	He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[18]	He W P, Deng B S, Wu Q, Zheng W, Cheng H Y 2010 Acta Phys. Sin. 59 8264 (in Chinese) [何文平, 邓北胜, 吴琼, 张文, 成海英 2010 59 8264]
[19]	Sun D Y, Zhang H B, Huang Q 2014 Acta Phys. Sin. 63 209203 (in Chinese) [孙东永, 张洪波, 黄强 2014 63 209203]
[20]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 57 1996]
[21]	He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 60 049202]
[22]	Held H, Kleinen T 2004 Geophysical Research Letters 31 L23207
[23]	Fisher R A 1922 Philos. Trans. R. Soc. Lond. Ser. A 222 309
[24]	Savit R, Green M 1991 Phys. D 50 95
[25]	Abaimov S G, Turcotte D L, Shcherbakov R, Rundle J B 2007 Non. Proc. Geophys. 14 455
[26]	Blender R, Fraedrich K, Sienz F 2008 Non. Proc. Geo. 15 557
[27]	Bunde A, Havlin S, Kantelhardt J W, Penzel T T, Peter J H, Voigt K 2000 Phys. Rev. Lett. 85 3736
[28]	Bunde A, Eichner J F, Kantelhardt J W, Havlin S 2005 Phys. Rev. Lett. 94 048701
[29]	Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[30]	Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 8 046133-1
[31]	Govindan R B, Vjushin D, Brenner S, Bunde A, Havlin S, Schellnhuber H J 2001 Phys. A 294 239
[32]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou Unibersity) p13 (in Chinese) [何文平 2008 博士论文 (兰州: 兰州大学) p13]
[33]	Peng C K, Buldyrev S V 1993 Phys. Rev. E 49 1685
[34]	Shiesinger M F, West B J, Klafter J 1987 Phys. Rev. Lett. 58 1100
[35]	Costas A Varotsos, Christian L E Franzke, Maria N Efstathiou, Andrei G Degermendzhi 2014 Theor. Appl. Climatol. 116 51
[36]	Chen Z, Ivanov P, Hu K, Stanley H E 2002 Physical Review E 65 041107
[37]	Hurst H 1951 Transactions of the American society of civil engineers 116 770
[38]	Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econometrics 112 265
[39]	He W P, Liu Q Q, Jiang Y D, Lu Y 2015 Chin. Phys. B 24 049205
[40]	Daniel L R, Russ E D 2003 Deep-Sea Reaearch Part I 50 691
[41]	Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[42]	Pincus S M 1995 J. Chaos 5 110
[43]	Pincus S M, Goldberger A L 1994 Am. J. Physiol. 266 H1643
[44]	Jin H M, He W P, Hou W, Zhang D Q 2012 Acta Phys. Sin. 61 069201 (in Chinese) [金红梅, 何文平, 侯威, 章大全 2012 61 069201]
[45]	Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese) [金红梅, 何文平, 张文, 冯爱霞, 侯威 2012 61 129202]
[46]	Frieden B R 1998 Physics from Fisher Information: A Unification (Cambridge: Cambridge University Press) pp319
[47]	Brian D F, Heriberto C, Christopher W P 2003 J. Theor. Biol. 222 517
[48]	Audrey L M, Christopher W P, Heriberto C 2006 Ecological Modelling 95 72
[49]	Julio R P, Deni T R, Luis R D, Joel T S, Francisco M P 2011 Entropy 13 1648
[50]	Yrulla L L, Giuliant A, Zbilut J P 1996 Phys. Lett. A 223 255
[51]	Gao J B, Cai H Q 2000 Phys. Lett. A 270 75
[52]	Provenzale A, Smith L A, Vio R, Murante G 1992 Physica D 58 31
[53]	Yu D J, Lu W P, Harrison R G 1999 J. Chaos 9 865
[54]	Schreiber T 1994 Phys. Rev. Lett. 78 843
[55]	Savit R, Green M 1991 Phys. D 50 95
[56]	Sauer T 1994 Phys. Rev. Lett. 72 3811
[57]	Grassberger P 1983 Phys. D 9 189
[58]	58 Li C G, Pei L Q 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵, 裴留庆 2003 52 2114]
[59]	Wan S Q, Feng G L, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5487 (in Chinese) [万仕全, 封国林, 董文杰, 李建平 2005 54 5487]
[60]	Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese) [龚志强, 封国林, 董文杰, 李建平 2006 55 3180]
[61]	Santer B D, Taylor K E, Wigley T M L, Penner J E, Jones P D, Cubasch U 1995 Clim. Dynam. 12 77
[62]	Santer B D, Taylor K E, Wigley T M L, Johns T C, Jones P D, Karoly D J, Mitchell J F B, Oort A H, Penner J E, Ramaswamy V, Schwarzkopf M D, Stouffer R J, Tett S 1996 Nature 382 39
[63]	Bernacchia A, Naveau P 2008 Nonlin. Processes Geophys. 15 159
[64]	Bernacchia A, Naveau P, Vrac M, Yiou P 2008 Nonlin. Processes Geophys. 15 169
[65]	Mocenni C, Facchini A, Vicino A 2010 Proceedings of the National Academy of Sciences of the United States of America 107 8097
[66]	Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta. Phys. Sin 54 5494 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2005 54 5494]
[67]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 50 606]
[68]	Feng G L, Dong W J, Jia X J 2004 Chin. Phys. 13 413

施引文献

[1]	Liu S D, Liu S K 1997 Chin. Sci. Bull. 42 1565 (in Chinese) [刘式达, 刘式适 1997 科学通报 42 1565]
[2]	Liu S D, Liu S K, Liang S, Ren K, Fu Z T 2002 Prog. Nat. Sci. 12 1 (in Chinese) [刘式达, 刘式适, 梁爽, 任奎, 付遵涛 2002 自然科学进展 12 1]
[3]	Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta. Phys. Sin 58 2853 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2009 58 2853]
[4]	Fu C B, Wang Q 1992 Chinese J. Atmos. Sci. 16 483 (in Chinese) [符淙斌, 王强 1992 大气科学 16 483]
[5]	Feng G L, Dong W J 2003 Chin. Phys. 12 1072
[6]	Feng G L, Dong W J, Li J P 2004 Chin. Phys. 13 1582
[7]	Li J P, Chou J F, Shi J E 1996 Journal of Beijing Meteorological college 2 16 (in Chinese) [李建平, 丑纪范, 史久恩 1996 北京气象学院 2 16]
[8]	Li J P, Shi J E 1993 Chinese J. Atmos. Sci. 17 132 (in Chinese) [李建平, 史久恩 1993 大气科学 17 132]
[9]	Xiao D, Li J P 2007 J. Geophys. Res. 112 D24S22
[10]	Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear theories and methods on spatial-temporal distribution of the obserbational data (Beijing: Metrological press) p27-89 [封国林, 董文杰, 龚志强, 侯威, 万仕全, 支蓉 2006 观测数据非线性时空分布理论和方法 (北京: 气象出版社)第 27–第89页]
[11]	Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[12]	Kendall M G 1970 Rank Correlation Methods (London: Charles Griffin)
[13]	Mann H B, Whitney D R 1947 Annals of Mathematical Statistics 18 50
[14]	Lepage 1971 Biometrika 58 213
[15]	He W P, Wan S Q, Jiang Y D, Jin H M, Zhang W, Wu Q, He T 2013 Int. J. Climatol. 33 2713
[16]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601
[17]	He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[18]	He W P, Deng B S, Wu Q, Zheng W, Cheng H Y 2010 Acta Phys. Sin. 59 8264 (in Chinese) [何文平, 邓北胜, 吴琼, 张文, 成海英 2010 59 8264]
[19]	Sun D Y, Zhang H B, Huang Q 2014 Acta Phys. Sin. 63 209203 (in Chinese) [孙东永, 张洪波, 黄强 2014 63 209203]
[20]	Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 57 1996]
[21]	He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 60 049202]
[22]	Held H, Kleinen T 2004 Geophysical Research Letters 31 L23207
[23]	Fisher R A 1922 Philos. Trans. R. Soc. Lond. Ser. A 222 309
[24]	Savit R, Green M 1991 Phys. D 50 95
[25]	Abaimov S G, Turcotte D L, Shcherbakov R, Rundle J B 2007 Non. Proc. Geophys. 14 455
[26]	Blender R, Fraedrich K, Sienz F 2008 Non. Proc. Geo. 15 557
[27]	Bunde A, Havlin S, Kantelhardt J W, Penzel T T, Peter J H, Voigt K 2000 Phys. Rev. Lett. 85 3736
[28]	Bunde A, Eichner J F, Kantelhardt J W, Havlin S 2005 Phys. Rev. Lett. 94 048701
[29]	Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[30]	Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 8 046133-1
[31]	Govindan R B, Vjushin D, Brenner S, Bunde A, Havlin S, Schellnhuber H J 2001 Phys. A 294 239
[32]	He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou Unibersity) p13 (in Chinese) [何文平 2008 博士论文 (兰州: 兰州大学) p13]
[33]	Peng C K, Buldyrev S V 1993 Phys. Rev. E 49 1685
[34]	Shiesinger M F, West B J, Klafter J 1987 Phys. Rev. Lett. 58 1100
[35]	Costas A Varotsos, Christian L E Franzke, Maria N Efstathiou, Andrei G Degermendzhi 2014 Theor. Appl. Climatol. 116 51
[36]	Chen Z, Ivanov P, Hu K, Stanley H E 2002 Physical Review E 65 041107
[37]	Hurst H 1951 Transactions of the American society of civil engineers 116 770
[38]	Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econometrics 112 265
[39]	He W P, Liu Q Q, Jiang Y D, Lu Y 2015 Chin. Phys. B 24 049205
[40]	Daniel L R, Russ E D 2003 Deep-Sea Reaearch Part I 50 691
[41]	Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[42]	Pincus S M 1995 J. Chaos 5 110
[43]	Pincus S M, Goldberger A L 1994 Am. J. Physiol. 266 H1643
[44]	Jin H M, He W P, Hou W, Zhang D Q 2012 Acta Phys. Sin. 61 069201 (in Chinese) [金红梅, 何文平, 侯威, 章大全 2012 61 069201]
[45]	Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese) [金红梅, 何文平, 张文, 冯爱霞, 侯威 2012 61 129202]
[46]	Frieden B R 1998 Physics from Fisher Information: A Unification (Cambridge: Cambridge University Press) pp319
[47]	Brian D F, Heriberto C, Christopher W P 2003 J. Theor. Biol. 222 517
[48]	Audrey L M, Christopher W P, Heriberto C 2006 Ecological Modelling 95 72
[49]	Julio R P, Deni T R, Luis R D, Joel T S, Francisco M P 2011 Entropy 13 1648
[50]	Yrulla L L, Giuliant A, Zbilut J P 1996 Phys. Lett. A 223 255
[51]	Gao J B, Cai H Q 2000 Phys. Lett. A 270 75
[52]	Provenzale A, Smith L A, Vio R, Murante G 1992 Physica D 58 31
[53]	Yu D J, Lu W P, Harrison R G 1999 J. Chaos 9 865
[54]	Schreiber T 1994 Phys. Rev. Lett. 78 843
[55]	Savit R, Green M 1991 Phys. D 50 95
[56]	Sauer T 1994 Phys. Rev. Lett. 72 3811
[57]	Grassberger P 1983 Phys. D 9 189
[58]	58 Li C G, Pei L Q 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵, 裴留庆 2003 52 2114]
[59]	Wan S Q, Feng G L, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5487 (in Chinese) [万仕全, 封国林, 董文杰, 李建平 2005 54 5487]
[60]	Gong Z Q, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 3180 (in Chinese) [龚志强, 封国林, 董文杰, 李建平 2006 55 3180]
[61]	Santer B D, Taylor K E, Wigley T M L, Penner J E, Jones P D, Cubasch U 1995 Clim. Dynam. 12 77
[62]	Santer B D, Taylor K E, Wigley T M L, Johns T C, Jones P D, Karoly D J, Mitchell J F B, Oort A H, Penner J E, Ramaswamy V, Schwarzkopf M D, Stouffer R J, Tett S 1996 Nature 382 39
[63]	Bernacchia A, Naveau P 2008 Nonlin. Processes Geophys. 15 159
[64]	Bernacchia A, Naveau P, Vrac M, Yiou P 2008 Nonlin. Processes Geophys. 15 169
[65]	Mocenni C, Facchini A, Vicino A 2010 Proceedings of the National Academy of Sciences of the United States of America 107 8097
[66]	Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta. Phys. Sin 54 5494 (in Chinese) [封国林, 王启光, 侯威, 龚志强, 支蓉 2005 54 5494]
[67]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林, 戴新刚, 王爱慧, 丑纪范 2001 50 606]
[68]	Feng G L, Dong W J, Jia X J 2004 Chin. Phys. 13 413

[1]	商继祥, 赵云波, 胡丽娜. 高温金属熔体黏度突变探索. , 2018, 67(10): 106402. doi: 10.7498/aps.67.20172721
[2]	孙东永, 张洪波, 王义民. 滑动移除小波分析法在动力学结构突变检验中的应用. , 2017, 66(7): 079201. doi: 10.7498/aps.66.079201
[3]	孙东永, 张洪波, 黄强. 滑动移除重标方差在动力学结构突变检验中的应用. , 2014, 63(20): 209203. doi: 10.7498/aps.63.209203
[4]	达朝究, 穆帅, 马德山, 于海鹏, 侯威, 龚志强. 基于Lorenz系统的数值天气转折期预报理论探索. , 2014, 63(2): 029201. doi: 10.7498/aps.63.029201
[5]	周守利, 李伽, 任宏亮, 温浩, 彭银生. 异质结界面电荷对突变InP/InGaAs异质结双极晶体管热场发射影响研究. , 2013, 62(17): 178501. doi: 10.7498/aps.62.178501
[6]	吴浩, 侯威, 王文祥, 颜鹏程. 试用Lyapunov指数探讨气候突变及其前兆信号. , 2013, 62(12): 129204. doi: 10.7498/aps.62.129204
[7]	吴浩, 封国林, 侯威, 颜鹏程. 中国不同区域气候突变的前兆信号. , 2013, 62(5): 059202. doi: 10.7498/aps.62.059202
[8]	吴浩, 侯威, 颜鹏程. 试用临界慢化原理探讨气候突变. , 2013, 62(3): 039206. doi: 10.7498/aps.62.039206
[9]	龚志强, 支蓉, 侯威, 王晓娟, 封国林. 基于复杂网络的北半球遥相关年代际变化特征研究. , 2012, 61(2): 029202. doi: 10.7498/aps.61.029202
[10]	吴浩, 侯威, 颜鹏程, 封国林. 基于临界慢化现象的气候突变前兆信号的初步研究. , 2012, 61(20): 209202. doi: 10.7498/aps.61.209202
[11]	吴勇峰, 张世平, 孙金玮, Peter Rolfe. 环形耦合Duffing振子间的同步突变. , 2011, 60(2): 020511. doi: 10.7498/aps.60.020511
[12]	何文平, 邓北胜, 吴琼, 张文, 成海英. 一种基于重标极差方法的动力学结构突变检测新方法. , 2010, 59(11): 8264-8271. doi: 10.7498/aps.59.8264
[13]	龚志强, 王晓娟, 支蓉, 封国林. 中国近58年温度极端事件的区域特征及其与气候突变的联系. , 2009, 58(6): 4342-4353. doi: 10.7498/aps.58.4342
[14]	何文平, 王启光, 吴琼, 张文, 张勇. 滑动去趋势波动分析与近似熵在动力学结构突变检测中的性能比较. , 2009, 58(4): 2862-2871. doi: 10.7498/aps.58.2862
[15]	王启光, 张增平. 近似熵检测气候突变的研究. , 2008, 57(3): 1976-1983. doi: 10.7498/aps.57.1976
[16]	刘迎辉, 李宏福, 李浩, 王峨锋, 徐勇, 王晖, 王丽. 具有突变结构开放腔的矩阵分析. , 2006, 55(4): 1718-1723. doi: 10.7498/aps.55.1718
[17]	龚志强, 封国林, 董文杰, 李建平. 非线性时间序列的动力结构突变检测的研究. , 2006, 55(6): 3180-3187. doi: 10.7498/aps.55.3180
[18]	封国林, 龚志强, 董文杰, 李建平. 基于启发式分割算法的气候突变检测研究. , 2005, 54(11): 5494-5499. doi: 10.7498/aps.54.5494
[19]	罗勇, 李宏福, 谢仲怜, 喻胜, 邓学, 赵青, 徐勇. 含有吸收介质的突变结构腔体场匹配分析. , 2004, 53(1): 229-234. doi: 10.7498/aps.53.229
[20]	李宏福, 杜品忠, 杨仕文, 谢仲怜, 周晓岚, 万洪蓉, 黄勇. 突变复合腔回旋管自洽场理论与模拟. , 2000, 49(2): 312-317. doi: 10.7498/aps.49.312

计量

文章访问数: 6901
PDF下载量: 387
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板