Prediction of smoothed monthly mean sunspot number based on chaos theory

Tang Jie; Zhang Xiong

doi:10.7498/aps.61.169601

Abstract

Long-term prediction of sunspot activity is of great importance for the space activity, communication, disaster prevention and so on. Cumulative error is main shortcoming of weighted one-rank local-region forecasting model for multi-steps prediction of chaotic time series. The radial basis function neural network forecasting model based on phase reconstruction is presented for chaotic time series prediction. The model is applied to the prediction of smoothed monthly mean sunspot numbers for the 22nd and 23rd sun cycles, and compared them with the observations. The results indicate that the mean absolute errors are 5.47 and 2.82, 15 to the maximum in absolute errors, and the mean relative errors are 5.45% and 4.60%, 15.00% to the maximum in relative errors. These results show that this prediction method can be successfully used to predict the smoothed monthly mean sunspot numbers. The predicted maximal smoothed monthly mean sunspot number is 104.77 that will appear in January 2013 for 132 months of cycle 24 from January 2009 to December 2019.

Keywords:

Authors and contacts

Tang Jie¹,
Zhang Xiong²

1.
School of Physics and Telecommunication Engineering, Shaanxi University of Technology, Hanzhong 723001, China;
2.
College of Physics and Electronics, Yunnan Normal University, Kunming 650092, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11163007) and the Key Program of the Natural Science Foundation of Yunnan Province, China (Grant No. 2008A011Z).

References

[1]	Lin Y Z 2000 Introduction to Solar Physics (Beijing: Science Press) p575 (in Chinese) [林元章 2000 太阳物理导论 (北京: 科学出版社) 第575页]
[2]	Wang J L, Miao J, Liu S Q, Gong J C, Zhu C L 2008 Sci. China Phys. Mech. Astron. 51 1938
[3]	Li K J, Qiu J, Xiang F Y, Gao P X, Su T W 2005 New Astron. 10 209
[4]	Tang J, Zhang X 2010 Acta Phys. Sin. 59 7516 (in Chinese) [唐洁, 张雄2010物理学报 59 7516]
[5]	Tang J, Zhang X, Wu L 2008 Chin. Astron. Astrophys. 32 151
[6]	Tang J, Zhang X J, Pang Q, Zhang H J, Zheng Y G, Zhang X 2010 Chin. Astron. Astrophys. 34 121
[7]	Li K J, Yun H S, Gu X M 2001 Astron. Astrophys. 368 285
[8]	Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer) p366
[9]	Meng Q F, Peng Y H, Qu H J, Han M 2008 Acta Phys. Sin. 57 1423 (in Chinese) [孟庆芳, 彭玉华,曲怀敬, 韩民 2008 物理学报 57 1423]
[10]	Ding G, Zhong S S 2007 Acta Phys. Sin. 56 1224 (in Chinese) [丁刚, 钟诗胜 2007 物理学报 56 1224]
[11]	Lü J H, Lu J A, Chen S H 2001 Analysis and Application of Chaotic Time Series (Wuhan: Wuhan University Press) p57 (in Chinese) [吕金虎, 陆君安, 陈士华 2001混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第57页]
[12]	Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[13]	Zhao H J, Wang J L, Zong W G, Tang Y Q, Le G M 2010 Chin. J. Geophys. 51 31 (in Chinese) [赵海娟,王家龙,宗位国,唐云秋,乐贵明 2010 地球物理学报 51 31]
[14]	Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys. Sin. 59 1576 (in Chinses) [张淑清,贾健,高敏,韩叙 2010 物理学报 59 1576]
[15]	Pesnell W D 2008 Solar Phys. 252 209
[16]	Wang J L, Zong W G, Le G M, Zhao H J, Tang Y Q, Zhang Y 2009 Res. Astron. Astrophys. 9 133
[17]	Li K J 2009 Res. Astron. Astrophys. 9 959
[18]	Li K J, Gao P X, Su T W 2005 Chin. J. Astron. Astrophys. 5 539

Cited By

[1]	Lin Y Z 2000 Introduction to Solar Physics (Beijing: Science Press) p575 (in Chinese) [林元章 2000 太阳物理导论 (北京: 科学出版社) 第575页]
[2]	Wang J L, Miao J, Liu S Q, Gong J C, Zhu C L 2008 Sci. China Phys. Mech. Astron. 51 1938
[3]	Li K J, Qiu J, Xiang F Y, Gao P X, Su T W 2005 New Astron. 10 209
[4]	Tang J, Zhang X 2010 Acta Phys. Sin. 59 7516 (in Chinese) [唐洁, 张雄2010物理学报 59 7516]
[5]	Tang J, Zhang X, Wu L 2008 Chin. Astron. Astrophys. 32 151
[6]	Tang J, Zhang X J, Pang Q, Zhang H J, Zheng Y G, Zhang X 2010 Chin. Astron. Astrophys. 34 121
[7]	Li K J, Yun H S, Gu X M 2001 Astron. Astrophys. 368 285
[8]	Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer) p366
[9]	Meng Q F, Peng Y H, Qu H J, Han M 2008 Acta Phys. Sin. 57 1423 (in Chinese) [孟庆芳, 彭玉华,曲怀敬, 韩民 2008 物理学报 57 1423]
[10]	Ding G, Zhong S S 2007 Acta Phys. Sin. 56 1224 (in Chinese) [丁刚, 钟诗胜 2007 物理学报 56 1224]
[11]	Lü J H, Lu J A, Chen S H 2001 Analysis and Application of Chaotic Time Series (Wuhan: Wuhan University Press) p57 (in Chinese) [吕金虎, 陆君安, 陈士华 2001混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第57页]
[12]	Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[13]	Zhao H J, Wang J L, Zong W G, Tang Y Q, Le G M 2010 Chin. J. Geophys. 51 31 (in Chinese) [赵海娟,王家龙,宗位国,唐云秋,乐贵明 2010 地球物理学报 51 31]
[14]	Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys. Sin. 59 1576 (in Chinses) [张淑清,贾健,高敏,韩叙 2010 物理学报 59 1576]
[15]	Pesnell W D 2008 Solar Phys. 252 209
[16]	Wang J L, Zong W G, Le G M, Zhao H J, Tang Y Q, Zhang Y 2009 Res. Astron. Astrophys. 9 133
[17]	Li K J 2009 Res. Astron. Astrophys. 9 959
[18]	Li K J, Gao P X, Su T W 2005 Chin. J. Astron. Astrophys. 5 539

[1]	Fang Bo-Lang, Wang Jian-Guo, Feng Guo-Bin. Calculation of spot entroid based on physical informed neural networks. Acta Physica Sinica, 2022, 71(20): 200601. doi: 10.7498/aps.71.20220670
[2]	Wei De-Zhi, Chen Fu-Ji, Zheng Xiao-Xue. Internet public opinion chaotic prediction based on chaos theory and the improved radial basis function in neural networks. Acta Physica Sinica, 2015, 64(11): 110503. doi: 10.7498/aps.64.110503
[3]	Xiu Chun-Bo, Liu Chang, Guo Fu-Hui, Cheng Yi, Luo Jing. Control strategy and application of hysteretic chaotic neuron and neural network. Acta Physica Sinica, 2015, 64(6): 060504. doi: 10.7498/aps.64.060504
[4]	Li Zhi-Jun, Zeng Yi-Cheng, Li Zhi-Bin. Memristive chaotic circuit based on modified SC-CNNs. Acta Physica Sinica, 2014, 63(1): 010502. doi: 10.7498/aps.63.010502
[5]	Chen Tie-Ming, Jiang Rong-Rong. New hybrid stream cipher based on chaos and neural networks. Acta Physica Sinica, 2013, 62(4): 040301. doi: 10.7498/aps.62.040301
[6]	Li He, Yang Zhou, Zhang Yi-Min, Wen Bang-Chun. Methodology of estimating the embedding dimension in chaos time series based on the prediction performance of radial basis function neural networks. Acta Physica Sinica, 2011, 60(7): 070512. doi: 10.7498/aps.60.070512
[7]	Li Hua-Qing, Liao Xiao-Feng, Huang Hong-Yu. Synchronization of uncertain chaotic systems based on neural network and sliding mode control. Acta Physica Sinica, 2011, 60(2): 020512. doi: 10.7498/aps.60.020512
[8]	Zhao Hai-Quan, Zhang Jia-Shu. Adaptive nonlinear channel equalization based on combination neural network for chaos-based communication systems. Acta Physica Sinica, 2008, 57(7): 3996-4006. doi: 10.7498/aps.57.3996
[9]	Wang Yong-Sheng, Sun Jin, Wang Chang-Jin, Fan Hong-Da. Prediction of the chaotic time series from parameter-varying systems using artificial neural networks. Acta Physica Sinica, 2008, 57(10): 6120-6131. doi: 10.7498/aps.57.6120
[10]	Wang Rui-Min, Zhao Hong. The role of neuron transfer function in artificial neural networks. Acta Physica Sinica, 2007, 56(2): 730-739. doi: 10.7498/aps.56.730
[11]	Zhao Hai-Quan, Zhang Jia-Shu, Zeng Xiang-Ping. Adaptive neural Legendre orthogonal polynomial nonlinear channel equalization for chaos-based communications systems. Acta Physica Sinica, 2007, 56(4): 1975-1982. doi: 10.7498/aps.56.1975
[12]	Peng Jian-Hua, Yu Hong-Jie. Associative memory and segmentation in the neural system under stimulation of stochastic or chaotic perceptual singals. Acta Physica Sinica, 2007, 56(8): 4353-4360. doi: 10.7498/aps.56.4353
[13]	Niu Pei_Feng, Zhang Jun, Guan Xin_Ping. Research on a proportional-integral-derivative neural network decoupling control based on genetic algorithm optimization for unified chaotic system. Acta Physica Sinica, 2007, 56(5): 2493-2497. doi: 10.7498/aps.56.2493
[14]	Xing Hong-Yan, Xu Wei. The neural networks method for detecting weak signals under chaotic background. Acta Physica Sinica, 2007, 56(7): 3771-3776. doi: 10.7498/aps.56.3771
[15]	Tan Wen, Wang Yao－Nan. Direct adaptive fuzzy-neural control of unknown chaotic system. Acta Physica Sinica, 2004, 53(12): 4087-4091. doi: 10.7498/aps.53.4087
[16]	Wang Yao-Nan, Tan Wen. Genetic-based neural network control for chaotic system. Acta Physica Sinica, 2003, 52(11): 2723-2728. doi: 10.7498/aps.52.2723
[17]	Ren Hai-Peng, Liu Ding. . Acta Physica Sinica, 2002, 51(5): 982-987. doi: 10.7498/aps.51.982
[18]	Tan Wen, Wang Yao-Nan, Liu Zhu-Run, Zhou Shao-Wu. . Acta Physica Sinica, 2002, 51(11): 2463-2466. doi: 10.7498/aps.51.2463
[19]	CHEN SHU, CHANG SHENG-JIANG, YUAN JING-HE, ZHANG YAN-XIN, K.W.WONG. ADAPTIVE TRAINING AND PRUNING FOR NEURAL NETWORKS:ALGORITHMS AND APPLICATION. Acta Physica Sinica, 2001, 50(4): 674-681. doi: 10.7498/aps.50.674
[20]	GUAN XIN-PING, TANG YING-GAN, FAN ZHENG-PING, WANG YI-QUN. NEURAL NERWORK BASED ROBUST ADAPTIVE SYNCHRONIZATION OF A CHAOTIC SYSTEM. Acta Physica Sinica, 2001, 50(11): 2112-2115. doi: 10.7498/aps.50.2112

Catalog

Vol. 61, Issue 16 - 2012-08-20

Metrics

Abstract views: 7786
PDF Downloads: 711
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板