New Approach to the Correlation Measurement for Subsystems in a Complex Giant System

LIN Yong-xin; CHEN Yu-shu; WANG Dan; CAO Qing-jie

doi:10.3879/j.issn.1000-0887.2013.09.005

Volume 34 Issue 9

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2013 > 34(9): 917-928

LIN Yong-xin, CHEN Yu-shu, WANG Dan, CAO Qing-jie. New Approach to the Correlation Measurement for Subsystems in a Complex Giant System[J]. Applied Mathematics and Mechanics, 2013, 34(9): 917-928. doi: 10.3879/j.issn.1000-0887.2013.09.005

Citation:

PDF( 2847 KB)

New Approach to the Correlation Measurement for Subsystems in a Complex Giant System

doi: 10.3879/j.issn.1000-0887.2013.09.005

College of Astronautics, Harbin Institute of Technology, Harbin 150001, P.R.China

Funds: The National Natural Science Foundation of China(10632040;1172065)

Received Date: 2013-04-08
Rev Recd Date: 2013-05-27
Publish Date: 2013-09-15

Abstract

Abstract

A nonlinear mutual prediction approach was presented to investigate the correlations and coupling strengths of nonlinear dependence among the subsystems in an open complex giant system, which behaved with complicated nonlinear dynamical characteristics. The time-varying discriminant values of mutual dependence obtained with the proposed method could be used to predict the correlations of the subsystems in a giant system based upon phase space reconstruction by using the observed small data and micro signal. Moreover, the obtained mechanism of interaction between the subsystems provides a nonlinear mutual prediction measurement, which is suitable for the analysis of financial crisis analytically.
- nonlinear mutual prediction approach,
- complex giant system,
- nonlinear dependent coupling strength,
- phase space reconstruction

FullText(HTML)

References(28)

References

[1]	Quyen M L V, Martinerie J, Adam C, Varela F J.Nonlinear analyses of interictal EEG map the brain interdependences in human focal epilepsy[J]. Physica D,1999,127(3/4)：250-266.
[2]	Amhold J, Grassberger P, Lehnertz K, Elger C E. A robust method for detecting interdependences：application to intracranially recorded EEG[J]. Physica D,1999,134：419-430.
[3]	Breakspear M, Terry J R. Detection and description of nonlinear interdependence in normal multichannel human EEG data[J]. Clinical Neurophysiology,2002,113(5): 735-753.
[4]	Radhakrishna R K A, Yeragani V K. Decreased chaos and increased nonlinearity of heart rate time series inpatients with panic disorder[J]. Auton Neurosci,2001,88(1/2): 99-108.
[5]	陆振波, 蔡志明, 姜可宇. 基于奇异值分解的混沌时间序列Volterra预测[J].武汉科技大学学报（交通科学与工程版）, 2007,31(4):672-675.(LU Zhen-bo, CAI Zhi-ming, JIANG Ke-yu. Prediction of chaotic time series using singular value decomposition Volterra filter[J]. Journal of Wuhan University of Technology (Transportation Science and Engineering),2007,31(4):672-675. (in Chinese))
[6]	Gu H, Wang H W. Fuzzy prediction of chaotic time series based on singular value decomposition[J]. Applied Mathematics and Computation,2007,185(2): 1171-1185.
[7]	DONG Xiao-meng, LUO Feng-juan, GUO Man-cai, YUAN Zhi-fa. Application of the autoregressive model of time series on the rainfall forecast of Yangling district[J]. Chinese Agricultural Science Bulletin,2007,23:403-407.
[8]	Landsamn A S , Schwartz I B. Complete chaotic synchronization in mutually coupled time-delayed system[J]. Physical Review E,2007,75(2): 1-8.
[9]	Schiff S J, So P, Chang T, Burke R E, Sauer T.Detecting dynamical interdependence and generalized synchorony through mutual prediction in a neural ensemble[J]. Physical Review E,1996,54(6)：6708-6724.
[10]	Rulkov N F, Sushchik M M, Tsimring L S, Abarbanel H D I.Generalized synchronization of chaos in directionally coupled chaotic systems[J]. Physical Review E,2005,51(2): 980-994.
[11]	Pompe B. Measuring statistical dependences in a time series[J].Journal of Statistical Physics,1993,73(3/4): 587-610.
[12]	Baele L, Inghelbrecht K. Timevarying integration, interdependence and contagion[J]. Journal of International Money and Finance,2010,29(5): 791-818.
[13]	Ang A, Bekaert G. International asset allocation with timevarying correlation[J].Review of Financial Studies,2002,15(4):1137-1187.
[14]	Pompe B, Blidh P, Hoyer D, Eiselt M.Using mutual information to measure coupling in the cardiores piratory system[J].IEEE Engineering in Medicine and Biology,1998,17(6): 32-39.
[15]	Hoyer D, Bauer R, Walter B, Zwiener U.Estimation of nonlinear couplings on the basis of complexity and predictability—a new method applied to cardiorespiratory coordination[J]. Transaction on Biomedical Engineering,1998,45(5)：545-552.
[16]	林勇新, 陈予恕, 曹庆杰. 一类金融系统行为的非线性混沌分析[J].应用数学和力学, 2010,31(10): 1239-1248.(LIN Yong-xin, CHEN Yu-shu, CAO Qing-jie. Nonlinear and chaotic analysis of a financial complicated system[J].Applied Mathematics and Mechanics, 2010,31(10)：1239-1248. (in Chinese))
[17]	马军海, 陈予恕. 低维混沌时序非线性动力系统的预测方法及其应用研究[J].应用数学和力学, 2001,22(5): 441-448.(MA Jun-hai, CHEN Yu-shu. Study on the prediction method of lowdimension time series that arise from the intrinsic non-linear dynamics [J]. Applied Mathematics and Mechanics, 2001,22 (5) : 441-448. (in Chinese))
[18]	马军海, 陈予恕, 辛宝贵. 基于非线性混沌时序动力系统的预测方法研究[J]. 应用数学和力学, 2004,25(6): 551557.(MA Jun-hai, CHEN Yu-shu, XIN Bao-gui. Study on prediction methods for dynamic systems of nonlinear chaotic time-series[J]. Applied Mathematics and Mechanics,2004,25(6) : 551-557. (in Chinese))
[19]	Castillo E, Gutierrez J M. Nonlinear time series modeling and prediction using functional networks extracting information masked by chaos[J]. Phys Lett A, 1998,244(5):71-84.
[20]	Schroer C G, Sauer T, Ott E, Yorke J A. Predicting chaotic most of the time from embeddings with self-intersections[J]. Phys Rev Lett,1998,80(7): 1410-1412.
[21]	马军海, 陈予恕, 刘曾荣. 动力系统实测数据的非线性混沌模型重构[J]. 应用数学和力学, 1999,20(11): 1128-1134.(MA Jun-hai, CHEN Yu-shu, LIU Zeng-rong. The nonlinear chaotic model reconstruction for the experimental data obtained from different dynamic system [J].Applied Mathematics and Mechanics,1999,20(11) : 1128-1134. (in Chinese))
[22]	Takens F. Detecting strange attractors in turbulence[J]. Lecture Notes in Mathematics,1981,898: 366-381.
[23]	Arthur W B. Complexity and the economy[J].Science,1999,284(5411):107-109.
[24]	Gelfand A E.Ensemble Modellng [M]. Marcel Dekker Inc, 1984.
[25]	米歇尔.沃尔德罗普. 复杂：诞生于秩序与混沌边缘的科学[M]. 陈玲译. 北京：三联书店出版社, 1998.(Michelle Waldrop.Complex: Science Origin From the Order and the Edge of Chaos [M]. CHEN Ling Trans. Beijng: SDX Joint Publishing Company, 1998. (in Chinese))
[26]	钱学森, 于景元, 戴汝为. 一个科学新领域——开放的复杂巨系统及其方法论[J].自然杂志, 1990,13(1)：1-10. (Tsien Hsue-shen, YU Jing-yuan, DAI Ru-wei .A new field of science—the study of open complex giant system and its methodology[J]. Chinese Journal of Nature,1991,13(1): 1-10.(in Chinese))
[27]	戴汝为. 复杂巨系统科学——一门21世纪的科学[J]. 自然杂志, 1997,19(4)：187-192.(DAI Ru-wei. Complex giant system science—a science of the 21st century[J]. Chinese Journal of Nature,1997,19(4): 187-192.(in Chinese))
[28]	Cao L Y, Mee A, Judd K. Dynamics from multivariate time series[J]. Physica D,1998,121(1/2):75-88.