Citation: | GAO Jianbo. Complex systems and emergence: How theory meets reality[J]. Advances in Mechanics, 2013, 43(4): 359-389. doi: 10.6052/1000-0992-13-046 |
[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.
|