Chaos and fractal properties of solar activity phenomena at the high and low latitudes

Zhou Shuang; Feng Yong; Wu Wen-Yuan

doi:10.7498/aps.64.249601

Abstract

The solar magnetic activity is produced by a complex dynamo mechanism and exhibits nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar activity phenomena are of great importance for understanding the nonlinear dynamo actions, especially nonlinear dynamo models. To study the chaotic and fractal properties of solar activity phenomena at the high-and low-latitudes, the polar faculae and sunspot numbers in the time interval from 1952 February to 1998 June are used to investigate their nonlinear dynamical behavior by the recurrence analysis method and Grassberger-Procaccia (G-P) algorithm. Firstly, the monthly average value of both polar faculae and sunspot numbers are smoothed to filter the noisy signal by the 13-point smoothing method. This procedure can keep the original dynamical information. Secondly, the correlation coefficient of these two solar activity indicators is analyzed, and the analysis results indicate that there is a negative correlation between polar faculae and sunspot numbers. To obtain more accurate results, the recurrence quantification analysis (RQA) is used to obtain the average value of the rate of DET by selecting four groups of different parameters. And then, we use the G-P algorithm to draw the correlation integral curve graphs and to obtain the correlation dimension of polar faculae and the sunspot numbers. Finally, the analysis results given by RQA and G-P algorithm are analyzed and compared by advanced statistical method. The main conclusions of this paper are as follows. 1) From a statistical point of view, the chaotic and fractal properties of high-and low-latitudes solar activity are different between in the northern hemisphere and in the southern hemisphere, owing to the fact that the temporal variation of solar activity is closely related to the magnetic field evolution. This result is in agreement with the previous results given by the polar faculae. It should be pointed out that this result is not the main goal of this article, we only reinforce this conclusion by the recurrence analysis and G-P algorithm. 2) The chaotic behaviors of solar magnetic activity at high latitude are stronger than at low latitude. Furthermore, the high-latitude solar activity in the northern hemisphere has the most complex fractal structure. Based on the solar nonlinear dynamo theory, the polar magnetic fields are the seed fields of the solar activity. That is to say, the physical meaning of polar faculae is more important than sunspot numbers. We think that our results are useful for understanding the physical nature of the systematic regularity of solar activity phenomena.

Keywords:

Authors and contacts

1.
Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China;
2.
University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Zhou Shuang, zhoushuang@cigit.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No.11301524) and the Chongqing Academicians Special Research Project Based on Basic and Frontier, China (Grant No. cstc2015jcyjys40001).

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[44]	Zbilut J P, Webber C L J 1992 Phys. Lett. A 171 199
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[47]	Grassberger P, Procaccia I 1983 Physica D 9 189
[48]	Watari S 1996 Sol. Phys. 63 259
[49]	Zhu H W 2004 Applied Statistics (Beijing: Higher Education Press) p155 (in Chinese) [朱洪文 2004 应用统计 (北京: 高等教育出版社) 第155 页]
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Cited By

[1]	Fang C, Ding M D, Chen P F 2008 Physics of Solar Active Regions (Nanjing: Nanjing University Press) p18 (in Chinese) [方成, 丁明德, 陈鹏飞 2008 太阳活动区物理 (南京:南京大学出版社) 第18 页]
[2]	Deng L H, Qu Z Q, Yan X L, Wang K R 2013 Res. Astron. Astrophys. 13 104
[3]	Chowdhury P, Khan M, Ray P C 2009 Mon. Not. R. Astron. Soc. 392 1159
[4]	Li K J, Feng W, Xu J C, Gao P X, Yang L H, Liang H F, Zhan L S 2012 Astrophys. J. 747 135
[5]	Qu Z N, Kong D F, Xiang N B, Feng W 2015 Astrophys. J. 798 113
[6]	Schatten K 2005 Geophys. Res. Lett. 32 L21106
[7]	Higgins P A, Gallagher P T, McAteer R J, Bloomfield D S 2011 Adv. Space Res. 47 2105
[8]	Friis-Christensen E, Lassen K 1991 Science 254 698
[9]	Lean J, Beer J, Bradley R 1995 Geophys. Res. Lett. 22 3195
[10]	Cherry N 2003 Nat. Hazards 29 1
[11]	Mendoza B, de la Pena S S 2010 Adv. Space Res. 46 449
[12]	Hanslmeier A, Brajsa R 2010 Astron. Astrophys. 509 A5
[13]	Spiegel E A 2009 Space Sci. Rev. 144 25
[14]	Zhou S, Feng Y, Wu W Y, Li Y, Liu J 2014 Res. Astron. Astrophys. 14 104
[15]	Li Q X, Li K J 2007 Chin. J. Astron. Astrophys. 7 435
[16]	Li Q X, Li K J 2007 Publ. Astron. Soc. Jpn. 59 983
[17]	Tang J, Zhang X 2012 Acta Phys. Sin. 61 169601 (in Chinese) [唐洁, 张雄 2012 物理学报 61 169601]
[18]	Zou P, Li Q X, Wu N 2014 Mon. Not. R. Astron. Soc. 2014 437 38
[19]	Deng L H, Li B, Xiang Y Y, Dun G T 2014 Adv. Space Res. 2014 54 125
[20]	Deng L H, Qu Z Q, Yan X L, Liu T, Wang K R 2012 J. Astrophys. Astron. 33 221
[21]	Deng L H, Qu Z Q, Yan X L, Liu T, Wang K R 2012 Astron. Nach. 33 221
[22]	Aschwanden M J, Aschwanden P D 2008 Astrophys. J. 674 530
[23]	Aschwanden M J, Aschwanden P D 2008 Astrophys. J. 674 544
[24]	Lepreti F, Fanello P C, Zaccaro F, Carbone V 2000 Sol. Phys. 197 149
[25]	Sen A K 2007 Sol. Phys. 241 67
[26]	Panchev S, Tsekov M 2007 J. Atmos. Sol. Terr. Phys. 69 2391
[27]	Deng L H, Song J Y, Xiang Y Y, Tang Y K 2011 J. Astrophys. Astron. 32 401
[28]	Deng L, Qu Z, Dun G, Xu C 2013 Publ. Astron. Soc. Jpn. 65 11
[29]	Zbilut J P, Giuliani A, Webber C L J 2000 Phys. Lett. A 267 174
[30]	Manetti C, Giuliani A, Ceruso M A, Webber C L J, Zbilut J P 2001 Phys. Lett. A 281 317
[31]	Thomasson N, Hoeppner T J, Webber C L J, Zbilut J P 2001 Phys. Lett. A 279 94
[32]	Webber C L J 2012 Front. Physiol. 3 382
[33]	Han G S, Yu Z G, Ann V 2011 Chin. Phys. B 20 100504
[34]	Liu J, Shi S T, Zhao J C 2013 Chin. Phys.B 22 010505
[35]	Meng Q F, Chen S S, Chen Y H, Feng Z Q 2014 Acta Phys. Sin. 63 050506 (in Chinese) [孟庆芳, 陈珊珊, 陈月辉, 冯志全 2014 物理学报 63 050506]
[36]	Ouyang G, Li X, Dang C, Richards D A 2008 Clin. Neurophysiol. 119 1747
[37]	Zhao P, Zhou Y L, Sun B 2010 J. Vibr. Measu. Diagn. 6 612 (in Chinese) [赵鹏,周云龙, 孙斌 2010 振动 · 测试与诊断 6 612]
[38]	Liu G L 2009 Acta Phys. Sin. 58 3359 (in Chinese) [刘贵立 2009 物理学报 58 3359]
[39]	Mandelbrot B B 1985 Phys. Scrip. 32 257
[40]	Badii R, Broggi G, Derighetti B, Ravani M, Ciliberto S, Politi A, Rubio M A 1988 Phys. Rev. Lett. 60 979
[41]	Grassberger P 1985 Phys. Lett. A 107 101
[42]	Li Q X 2008 Ph. D. Dissertation (Kunming: Yunnan Observatories Chinese Academy of Sciences) (in Chinese) [李启秀 2008 博士论文 (昆明: 中国科学院云南天文台)]
[43]	Echmann J P, Kamphorst S O, Ruelle D 1987 Europhys. Lett. 4 973
[44]	Zbilut J P, Webber C L J 1992 Phys. Lett. A 171 199
[45]	Webber C L J, Zbilut J P 1994 J. Appl. Physiol. 76 965
[46]	Grassberger P, Procaccia I 1983 Phys. Rev. Lett. 50 346
[47]	Grassberger P, Procaccia I 1983 Physica D 9 189
[48]	Watari S 1996 Sol. Phys. 63 259
[49]	Zhu H W 2004 Applied Statistics (Beijing: Higher Education Press) p155 (in Chinese) [朱洪文 2004 应用统计 (北京: 高等教育出版社) 第155 页]
[50]	Yang X Y, Xiang S P, Chen Q D 2014 Statistics and Decision 9 78 (in Chinese) [杨湘豫, 向圣鹏, 陈前达 2014 统计与决策 9 78]

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Vol. 64, Issue 24 - 2015-12-20

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