复杂系统和涌现: 理论如何与现实结合

高剑波

doi:10.6052/1000-0992-13-046

复杂系统和涌现: 理论如何与现实结合

doi: 10.6052/1000-0992-13-046

高剑波^1,2, ,

1.
PMB Intelligence LLC, Sunnyvale, CA 94087, USA
2.
Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435, USA

详细信息

通讯作者:
高剑波

中图分类号: N941.4 O414.2
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出版历程
- 收稿日期: 2013-06-10
- 刊出日期: 2013-07-25

Complex systems and emergence: How theory meets reality

GAO Jianbo^{1,2
, ,}

1.
PMB Intelligence LLC, Sunnyvale, CA 94087, USA
2.
Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435, USA

More Information

Corresponding author: GAO Jianbo

摘要

摘要: 复杂系统所表现出的涌现行为吸引了人类极长时间的关注. 然而只是在近几十年来, 大量的工作才对这些行为进行了定量的研究, 并发展出许多重要的理论和方法, 比如混沌理论, 随机分形理论以及多尺度分析. 本文旨在对这个广阔研究领域内最好的研究和实践进行介绍, 并着重强调了理论如何与实际问题相结合. 作为说明的例子, 对网络安全、经济危机、河流动力学以及世界范围内的政治冲突进行了简要讨论. 也列举了未来几个重要研究方向.
- 复杂系统 /
- 涌现 /
- 混沌 /
- 分形 /
- 网络安全 /
- 经济危机 /
- 河流动力学 /
- 政治冲突
Abstract: Emergent behaviors of complex systems have fascinated mankind for aeons. It is only in recent decades that extensive efforts have been made to quantitatively study them, resulting in important theories and tools such as chaos theory, random fractal theory, and multiscale analyses. This article aims to convey the best practices in this vast field, emphasizing theory meets reality. As illustrative examples, cyber-security, financial crises, river flow dynamics, and world-wide political conflicts will be briefly discussed. Important future research directions will also be outlined.
- complex systems /
- emergence /
- chaos /
- fractal /
- cyber security /
- financial crisis /
- river dynamics /
- political conflicts

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参考文献(100)

[1]	Amaral L A N, Goldberger A L, Ivanov P C, Stanley H E, 1998. Scale-independent measures and pathologic cardiac dynamics. Phys. Rev. Lett., 81: 2388.
[2]	Anderson D, Frivold T, Valdes A, 1995. Next generation Intrusion Detection Expert System (NIDES): A summary, Technical Report SRI-CSL-97-07, Menlo Park, Calif,: SRI Int’l.
[3]	Anderson P L, Meerschaert M M, 1998. Modeling river flows with heavy tails. Water Resources Research, 34: 2271-2280.
[4]	Aurell E, Boffetta G, Crisanti A, Paladin G, Vulpiani A, 1996. Growth of non-infinitesimal perturbations in turbulence. Phys. Rev. Lett., 77: 1262.
[5]	Aurell E, Boffetta G, Crisanti A, Paladin G, Vulpiani A, 1997. Predictability in the large: An extension of the concept of Lyapunov exponent. J. Physics A, 30: 1-26.
[6]	Bar-Yam Y, 1992. Dynamics of Complex Systems, Addison-Wesley, Reading, Massachusetts.
[7]	Bernaola-Galvan P, Ivanov P C, Amaral L A N, Stanley H E, 2001. Scale invariance in the nonstationarity of human heart rate. Phys. Rev. Lett., 87: 168105.
[8]	Boccara N, 2010. Modeling Complex Systems, 2nd Ed., Springer.
[9]	Box G E P, Jenkins G M, 1976. Time Series Analysis: Forecasting and Control. 2nd ed. San Francisco: Holden- Day.
[10]	Bussiere M, Fratzscher M, 2002. Towards a new early warning system of financial crises, European Central Bank Working Paper No.145.
[11]	Chen Y Q, Ding M Z, Scott Kelso J A, 1997. Long memory processes ( 1/f Type) in human coordination. Phys. Rev. Lett., 79: 4501.
[12]	Collins J J, De Luca C J, 1994. Random walking during quiet standing. Phys. Rev. Lett., 73: 764.
[13]	Cox D R, 1984. Long-range dependence: A review. In: Statistics, An Appraisal. (David, H.A. & Davis, H.T. eds.) 55-74, Iowa: Iown State Univ. Press
[14]	Darwin C, 1859. On The Origin of Species. London, John Murray
[15]	De Domenico D M, Latora V, 2011. Scaling and universality in river flow dynamics, EPL, 94: doi:10.1209/0295- 5075/94/58002.
[16]	D’Orsogna M R, Chuang Y L, Bertozzi A L, Chayes L S, 2006. Self-propelled particles with soft-core interactions: Patterns, stability, and collapse. Physical Review Let- ters, 96: 10.
[17]	Forrest S, Hofmeyr S A, Somayaji A, Longstaff T A, 1996. A sense of self for Unix processes, in: Proceedings of the 1996 IEEE Symposium on Research in Security and Privacy, Los Alamos, CA, 120-128.
[18]	Fraser A, Swinney H, 1986. Independent coordinates for strange attractors from mutual information, Phys. Rev. A, 33: 1134-1140.
[19]	Frisch U, 1995. Turbulence—The Legacy of A.N. Kolmogorov. Cambridge University Press.
[20]	Gao J B, Zheng Z M, 1993. Local exponential divergence plot and optimal embedding of a chaotic time series. Phys. Lett. A, 181: 153-158.
[21]	Gao J B, Zheng Z M, 1994a. Direct dynamical test for deterministic chaos. Europhys. Lett., 25: 485-490.
[22]	Gao J B, Zheng Z M, 1994b. Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series. Phys. Rev. E, 49: 3807-3814.
[23]	Gao J B, 1997. Recognizing randomness in a time series. Physica D, 106: 49.
[24]	Gao J B, Hwang S K, Liu J M, 1999a. When can noise induce chaos? Phys. Rev. Lett., 82: 1132.
[25]	Gao J B, Chen C C, Hwang S K, Liu J M, 1999b. Noiseinduced chaos. Int. J. Mod. Phys. B, 13: 3283.
[26]	Gao J B, Rubin I, 2001a. Multiplicative multifractal modeling of long-range-dependent network traffic. Int. J. Comm. Systems, 14: 783-801.
[27]	Gao J B, Rubin I, 2001b. Multifractal modeling of counting processes of long-range-dependent network Traffic. Computer Communications, 24: 1400-1410.
[28]	Gao J B, Rao J S V, Hu J, Ai J, 2005a. Quasi-periodic route to chaos in the dynamics of Internet transport protocols. Phys. Rev. Lett., 94: 198702.
[29]	Gao J B, Qi Y, Cao Y H, Tung W W, 2005b. Protein coding sequence identification by simultaneously characterizing the periodic and random features of dna sequences. Journal of Biomedicine and Biotechnology, 2: 139-146.
[30]	Gao J B, Billock V, Merk I, et al. 2006a. Inertia and memory in ambiguous visual perception. Cognitive Pro- cessing, 7: 105-112.
[31]	Gao J B, Hu J, Tung W W, Cao Y H, Sarshar N and Roychowdhury Vwani P. 2006b. Assessment of long range correlation in time series: How to avoid pitfalls. Phys. Rev. E, 73: 016117.
[32]	Gao J B, Hu J, TungWW, Cao Y H, 2006c. Distinguishing chaos from noise by scale-dependent Lyapunov exponent. Phys. Rev. E, 74: 066204.
[33]	Gao J B, Cao Y H, Tung W W, Hu J, 2007. Multiscale Analysis of Complex Time Series — Integration of Chaos and Random Fractal Theory, and Beyond, Wiley.
[34]	Gao J B, Tung W W, Hu J, 2009. Quantifying dynamical predictability: The pseudo-ensemble approach (in honor of Professor Andrew Majda’s 60th birthday). Chinese Annals. Math. Series B, 30: 569-588.
[35]	Gao J B, Sultan H, Hu J, Tung W W, 2010. Denoising nonlinear time series by adaptive filtering and wavelet shrinkage: A comparison. IEEE Signal Processing Let- ters, 17: 237-240.
[36]	Gao J B, Hu J, Tung W W, 2011a. Facilitating joint chaos and fractal analysisof biosignals through nonlinear adaptive filtering. PLoS ONE, 6: e24331.
[37]	Gao J B, Hu J, Tung W W, 2011b. Complexity measures of brain wave dynamics. Cognitive Neurodynamics, 5: 171-182.
[38]	Gao J B, Hu J, Mao X, Zhou M, Gurbaxani B, Lin J W B, 2011c. Entropies of negative incomes, Pareto-distributed loss, and financial crises. PLoS ONE, 6: e25053.
[39]	Gao J B, Hu J, Mao X, Perc M, 2012a. Culturomics meets random fractal theory: Insights into longrange correlations of social and natural phenomena over the past two centuries. J. Royal Society Interface, doi: 10.1098/rsif.2011.0846.
[40]	Gao J B, Hu J, Mao X, Tung W W, 2012b. Detecting low-dimensional chaos by the “noise titration” technique: possible problems and remedies. Chaos, Solitons, & Fractals, 45: 213-223.
[41]	Gao J B, Hu J, Tung W W, Blasch E, 2012c. Multiscale analysis of physiological data by scale-dependent Lyapunov exponent. Frontiers in Fractal Physiology, doi: 10.3389/fphys.2011.00110.
[42]	Gao J B, Hu J, Tung W W, Zheng Y, 2013. Multiscale analysis of economic time series by scale-dependent Lyapunov exponent. Quantitative Finance, 13: 265-274.
[43]	Gilden D L, Thornton T, Mallon M W, 1/f noise in human cognition. 1995. Science , 267: 1837.
[44]	Goldberger A S, 1972. Structural equation methods in the social sciences. Econometrica, 40: 979-1001.
[45]	Goldstein J S, 1992. A conflict-cooperation scale for WEIS events data. Journal of Con ict Resolution, 36: 369-385.
[46]	Hemelrijk C K, Hildenbrandt H, 2007. Self-organized shape and frontal density of fish schools. Ethology, 114: 3.
[47]	Hemelrijk C K, Hildenbrandt H, 2011. Some causes of the variable shape of flocks of birds. PLoS ONE, 6: e22479.
[48]	Hildenbrandt H, Carere C, Hemelrijk C K, 2010. Selforganized aerial displays of thousands of starlings: a model. Behavioral Ecology, 21: 1349-1359.
[49]	Hu J, Gao J B, Cao Y H, Bottinger E, Zhang W, 2007. Exploiting noise in array cgh data to improve detection of dna copy number change. Nucleic Acids Research, 35: e35.
[50]	Hu J, Gao J B, Tung W W, 2009a. Characterizing heart rate variability by scale-dependent Lyapunov exponent. Chaos, 19: 028506.
[51]	Hu J, Gao J B, Wang X S, 2009b. Multifractal analysis of sunspot time series: the effects of the 11-year cycle and Fourier truncation. J. Statistical Mech., 02/P02066.
[52]	Hu J, Gao J B, TungWW, Cao Y H, 2010. Multiscale analysis of heart rate variability: A comparison of different complexity measures Annals of Biomedical Engineering, 38: 854-864.
[53]	Islam M N, Sivakumar B, 2002. Characterization and prediction of runoff dynamics: a nonlinear dynamical view. Adv. Water Res., 25: 179.
[54]	Ivanov P C, Rosenblum M G, Peng C K, Mietus J, Havlin S, Stanley H E, Goldberger A L, 1996. Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis. Nature, 383: 323.
[55]	Ivanov P C, Rosenblum M G, Amaral L A N, Struzik Z R, Havlin S, Goldberger A L, Stanley H E, 1999. Multifractality in human heartbeat dynamics. Nature, 399: 461.
[56]	Kastens K A, Manduca C A, Cervato C, et al. 2009. How geoscientists think and learn. Eos, Trans. American Geophy. Union. 90: 265-272.
[57]	Kennel M, Brown R, Abarbanel H, 1992. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A, 45: 3403- 3411.
[58]	Kroy K, Sauermann G, Herrmann H J, 2002. Minimal model for sand dunes. Physical Review Letters, 88: 054301.
[59]	Kruegel C, Vigna G, 2003. Anomaly detection of web-based attacks, in: Proceedings of the 10th ACM Conference on Computer and Communication Security (CCS 2003).
[60]	Washington D.C., USA: ACM Press, Oct. 2003, 251-261.
[61]	Kuznetsov N, Bonnette S, Gao J B, Riley M A, 2012. Adaptive fractal analysis reveals limits to fractal scaling in center of pressure trajectories. Annals of Biomedical En- gineering, DOI 10.1007/s10439-012-0646-9.
[62]	Liebert W, Pawelzik K, Schuster H, 1991. Optimal embedding of chaotic attractors from topological considerations. Europhys. Lett., 14: 521-526.
[63]	Li W, Kaneko K, 1992. Long-range correction and partial 1/f = spectrum in a noncoding DNA sequence. Euro- phys. Lett., 17: 655.
[64]	Lin C C, Shu F H, 1964. On the spiral structure of disk galaxies. The Astrophysical Journal, 140: 646-655.
[65]	Mandelbrot B B, 1982. The Fractal Geometry of Nature. San Francisco: Freeman.
[66]	Manyika J, Chui M, Brown B, Bughin J, Dobbs R, Roxburgh C, Byers A H, 2011. Big data: The next frontier for innovation, competition, and productivity. http://www.mckinsey.com/insights/mgi/research/ technology and innovation/big data the next frontier for innovation
[67]	Osborne A R, Provenzale A, 1989. Finite correlation dimension for stochastic-systems with power-law spectra. Physica D, 35: 357-381.
[68]	Packard N H, Crutchfield J P, Farmer J D, Shaw R S, 1980.Geometry from a time series. Phys. Rev. Lett., 45: 712- 716.
[69]	Peng C K, Buldyrev S V, Goldberger A L, Havlin S, Sciortino F, Simons M, Stanley H E, 1992. Long-range correlations in nudeotide sequences. Nature, 356: 168.
[70]	Peng C K, Buldyrev S V, Harlin S, Simons M, Stanley H E and Goldberger A L. 1994. Mosaic organization of dna nucleotides. Phys. Rev. E, 49: 1685-1689.
[71]	Pomeau Y, Manneville P, 1980. Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys., 74: 189-197.
[72]	Provenzale A, Osborne A R, Soj R, 1991. Convergence of the K2 entropy for random noises with power law spectra. Physica D, 47: 361-372.
[73]	Reinhart C M, Rogoff K S, 2008. Is the 2007 US sub-prime financial crisis so different? An international historical comparison. American Economic Review, 98: 339-344.
[74]	Reynolds C W, 1987. Flocks, herds and schools: A distributed behavioral model. Computer Graphics, 21: 25- 34.
[75]	Riley M A, Kuznetsov N, Bonnette S, Wallot S, Gao J B, 2012. A tutorial introduction to adaptive fractal analysis. Frontiers in Fractal Physiology, doi: 10.3389/fphys.2012.00371.
[76]	Rose A K, Spiegel M M, 2009. Cross-Country Causes and Consequences of the 2008 Crisis: Early Warning, CEPR Discussion Paper 7354.
[77]	Ruelle D, Takens F, 1971. On the nature of turbulence. Commun. Math. Phys., 20: 167.
[78]	Ryan D A, Sarson G R, 2008. The geodynamo as a lowdimensional deterministic system at the edge of chaos. EPL, 83: 49001.
[79]	Sauer T, Yorke J A, Casdagli M, 1991. Embedology. J. Stat. Phys., 65: 579-616.
[80]	Scheffer M, Carpenter S R, Lenton T M, Bascompte J, Brock W, Dakos V, Koppel Johan van de Kopper et al. 2012. Anticipating critical transitions. Science, 338: 344-349.
[81]	Schrodt P A, Gerner D J, Ömür G, 2009. Conflict and mediation event observations (CAMEO): an event data frameworkfor a post cold war world. in(eds. Bercovitch, J. & Gartner, S.): International Conflict Mediation: New Approaches and Findings, Routledge, New York.
[82]	Shaw E, 1978. Schooling fishes. American Scientist, 66: 166-175.
[83]	Sivakumar B, 2004. Chaos theory in geophysics: Past, present and future. Chaos, Solitons Fractals, 19: 441- 462.
[84]	Solow R, 1956. A contribution to the theory of economic growth. Quarterly Journal of Economics (The MIT Press), 70: 65-94.
[85]	Swan T, 1956. Economic growth and capital accumulation. Economic Record, 32: 334-361.
[86]	Takens F, 1981. Detecting strange attractors in turbulence, in (eds. Rand, D.A. & Young, L.S.): Dynamical Systems and Turbulence, Lecture Notes in Mathematics, Vol.898, Springer-Verlag, Berlin, pp. 366.
[87]	Tessier Y, Lovejoy S, Hubert P, Schertzer D, Pecknold S, 1996. Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions. J. Geo- phys. Res. Atmos., 101: 26427.
[88]	Torcini A, Grassberger P, Politi A, 1995. Error propagation in extended chaotic systems. J. Phys. A: Mathematical and General, 28: 4533.
[89]	Tung W W, Gao J B, Hu J, Yang L, 2011. Recovering chaotic signals in heavy noise environments. Phys. Rev. E, 83: 046210.
[90]	Turnovsky S J, 2000. Methods of Macroeconomic Dynamics, MIT Press.
[91]	Vasavada A R, Showman A, 2005. Jovian atmospheric dynamics: An update after Galileo and Cassini. Reports on Progress in Physics, 68: 1935-1996.
[92]	Voss R F, 1992. Evolution of long-range fractal correlations and 1/f noise in DNA base sequences. Phys. Rev. Lett., 68: 3805.
[93]	Wang K, Stolfo S J, 2004. Anomalous payload-based network intrusion detection, in: 7th International Symposium on Recent Advances in Intrusion Detection (RAID 2004), Sophia Antipolis, French Riviera, France.
[94]	Wang W, Vrijling J K, Van Gelder P H A J M, Ma J, 2006. Testing for nonlinearity of streamflow processes at different timescales. Journal of Hydrology, 322: 247-268.
[95]	Warrender C, Forrest S, Pearlmutter B, 1999. Detecting intrusions using system calls: Alternative data models, in: Proceedings of 1999 IEEE Symposium on Security and Privacy, 133-145.
[96]	Wolf M, 1997. 1/f noise in the distribution of prime numbers. Physica A, 241: 493.
[97]	Wolf A, Swift J B, Swinney H L, Vastano J A, 1985. Determining Lyapunov exponents from a time series. Physica D, 16: 285-317.
[98]	Yan Q, Xie W, Yan B, Song G, 2002. An anomaly intrusion detection method based on HMM. Electronics Letters, 38: 663-664.
[99]	Ye N, Zhang Y, Borror C M, 2004. Robustness of the Markov chain model for cyber attack detection. IEEE Transactions on Reliability, 51: 116-121.
[100]	Zhang G M, Yu L, 2010. Emergent phenomena in physics. Physics (in Chinese), 39: 543.