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Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

  • J. A. Tenreiro Machado EMAIL logo und António M. Lopes
Veröffentlicht/Copyright: 13. März 2015
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Abstract

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

References

[1] L. A. N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley, Classes of small-world networks. Proc. of the National Academy of Sciences 97, No 21 (2000), 11149-11152. Suche in Google Scholar

[2] A. Arenas, L. Danon, A. Diaz-Guilera, P. M. Gleiser, and R. Guimera, Community analysis in social networks. The European Physical J. BCondensed Matter and Complex Systems 38, No 2 (2004), 373-380.Suche in Google Scholar

[3] W. B. Arthur, Complexity and the economy. Science 284, No 5411 (1999), 107-109.Suche in Google Scholar

[4] D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods. Ser. on Complexity, Nonlinearity and Chaos, World Scientific (2012).10.1142/8180Suche in Google Scholar

[5] A.-L. Barabási, H. Jeong, Z. Néda, E. Ravasz, A. Schubert, and T. Vicsek, Evolution of the social network of scientific collaborations. Physica A: Statistical Mechanics and its Applications 311, No 3 (2002), 590-614.Suche in Google Scholar

[6] D. S. Bassett and E. Bullmore, Small-world brain networks. The Neuroscientist 12, No 6 (2006), 512-523.Suche in Google Scholar

[7] P. Bhattacharya, B. K. Chakrabarti, and Kamal, A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data. Journal of Physics: Conference Series 319, No 1 (2011), 1012004.Suche in Google Scholar

[8] C. M. Bishop, Pattern Recognition and Machine Learning, Springer, New York (2006).Suche in Google Scholar

[9] T. F. Cox andM. A. Cox, Multidimensional Scaling, CRC Press (2000). 10.1201/9781420036121Suche in Google Scholar

[10] J. Foster, From simplistic to complex systems in economics. Cambridge J. of Economics 29, No 6 (2005), 873-892.Suche in Google Scholar

[11] T. J. Foxon, J. Köhler, J. Michie, and C. Oughton, Towards a new complexity economics for sustainability. Cambridge J. of Economics 37, No 1 (2013), 187-208.Suche in Google Scholar

[12] A. L. Goldberger, L. A. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, J. E.Mietus, G. B. Moody, C.-K. Peng, and H. E. Stanley, Physiobank, physiotoolkit, and physionet components of a new research resource for complex physiologic signals. Circulation 101, No 23 (2000), e215-e220.Suche in Google Scholar

[13] F. Guzzetti, B. D. Malamud, D. L. Turcotte, and P. Reichenbach, Power-law correlations of landslide areas in central Italy. Earth and Planetary Science Letters 195, No 3 (2002), 169-183.Suche in Google Scholar

[14] H. Haken, Information and Self-Organization: A Macroscopic Approach to Complex Systems. Springer (2006).Suche in Google Scholar

[15] W.-Q. Huang, X.-T. Zhuang, and S. Yao, A network analysis of the chinese stock market. Physica A: Statistical Mechanics and its Applications 388, No 14 (2009), 2956-2964.Suche in Google Scholar

[16] C. M. Ionescu, The Human Respiratory System: An Analysis of the Interplay between Anatomy, Structure, Breathing and Fractal Dynamics. Springer (2013).Suche in Google Scholar

[17] A. K. Jain, Data clustering: 50 years beyond k-means. Pattern Recognition Letters 31, No 8 (2010), 651-666.Suche in Google Scholar

[18] N. F. Johnson, P. Jefferies, and P. M. Hui, Financial market complexity. OUP Catalogue (2003).10.1093/acprof:oso/9780198526650.001.0001Suche in Google Scholar

[19] A. Kato, J. Murai, S. Katsuno, and T. Asami, An internet traffic data repository: The architecture and the design policy. In: INET’99 Proceedings (1999).Suche in Google Scholar

[20] M. S. Keshner, 1/f noise. Proceedings of the IEEE 70, No 3 (1982), 212-218.Suche in Google Scholar

[21] K. Kiyono, Z. R. Struzik, N. Aoyagi, F. Togo, and Y. Yamamoto, Phase transition in a healthy human heart rate. Physical Review Letters 95, No 5 (2005), 058101.10.1103/PhysRevLett.95.058101Suche in Google Scholar PubMed

[22] S. Lennartz, V. Livina, A. Bunde, and S. Havlin, Long-term memory in earthquakes and the distribution of interoccurrence times. EPL (Europhysics Letters) 81, No 6 (2008), 69001.10.1209/0295-5075/81/69001Suche in Google Scholar

[23] W. Li and X. Cai, Statistical analysis of airport network of China. Physical Review E 69, No 4 (2004), 046106.10.1103/PhysRevE.69.046106Suche in Google Scholar PubMed

[24] W. Li, X. Zhang, and G. Hu, How scale-free networks and large-scale collective cooperation emerge in complex homogeneous social systems. Physical Review E 76, No 4 (2007), 045102. 10.1103/PhysRevE.76.045102Suche in Google Scholar PubMed

[25] G. Lim, S. Kim, J. Kim, P. Kim, Y. Kang, S. Park, I. Park, S.-B. Park, and K. Kim, Structure of a financial cross-correlation matrix under attack. Physica A: Statistical Mechanics and its Applications 388, No 18 (2006), 3851-3858.Suche in Google Scholar

[26] M. Lima, J. A. Tenreiro Machado, and A. C. Costa, A multidimensional scaling analysis of musical sounds based on pseudo phase plane. Abstract and Applied Analysis 2012 (2012), 436108.10.1155/2012/436108Suche in Google Scholar

[27] A. M. Lopes and J. T. Machado, Dynamical behaviour of multi-particle large-scale systems. Nonlinear Dynamics 69, No 3 (2012), 913-925.Suche in Google Scholar

[28] A. M. Lopes and J. Tenreiro Machado, Analysis of temperature timeseries: Embedding dynamics into the mds method. Communications in Nonlinear Science and Numerical Simulation 19, No 4 (2014), 851-871.Suche in Google Scholar

[29] J. A. T. Machado and A. M. Lopes, Analysis and visualization of seismic data using mutual information. Entropy 15, No 9 (2013), 3892-3909.Suche in Google Scholar

[30] J. T. Machado, And I say to myself: “What a fractional world!”. Fractional Calculus and Applied Analysis 14, No 4 (2011), 635-654; DOI: 10.2478/s13540-011-0037-1; http://link.springer.com/article/10.2478/s13540-011-0037-1.Suche in Google Scholar

[31] D. Makowiec, A. Dudkowska, R. Ga_laska, and A. Rynkiewicz, Multifractal estimates of monofractality in RR-heart series in power spectrum ranges. Physica A: Statistical Mechanics and its Applications 388, No 17 (2009), 3486-3502.Suche in Google Scholar

[32] B. B. Mandelbrot, The Fractal Geometry of Nature. Macmillan (1983).10.1119/1.13295Suche in Google Scholar

[33] B. B. Mandelbrot and J. W. Van Ness, Fractional brownian motions, fractional noises and applications. SIAM Review 10, No 4 (1968), 422-437.Suche in Google Scholar

[34] R. Mategna and H. Stanley, An Introduction to Econophysics. Cambridge University (2000).Suche in Google Scholar

[35] Z. M’Chirgui, Small-world or scale-free phenomena in internet: What implications for the next-generation networks? Review of European Studies 4, No 1 (2012), 85-93; DOI: 10.5539/res.v4n1p85.10.5539/res.v4n1p85Suche in Google Scholar

[36] A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations- Concepts and Applications of Voronoi Diagrams. John Wiley (2000).10.1002/9780470317013Suche in Google Scholar

[37] C. Pinto, A. Mendes Lopes, and J. Machado, A review of power laws in real life phenomena. Communications in Nonlinear Science and Numerical Simulation 17, No 9 (2012), 3558-3578.Suche in Google Scholar

[38] D. Rind, Complexity and climate. Science 284, No 5411 (1999), 105-107.Suche in Google Scholar

[39] T. Robertazzi and P. Sarachik, Self-organizing communication networks. Communications Magazine, IEEE 24, No 1 (1986), 28-33. [40] M. Sachtjen, B. Carreras, and V. Lynch, Disturbances in a power transmission system. Physical Review E 61, No 5 (2000), 4877.Suche in Google Scholar

[41] L. A. Schintler, S. P. Gorman, A. Reggiani, R. Patuelli, A. Gillespie, P. Nijkamp, and J. Rutherford, Complex network phenomena in telecommunication systems. Networks and Spatial Economics 5, No 4 (2005), 351-370.Suche in Google Scholar

[42] P. Sen, S. Dasgupta, A. Chatterjee, P. Sreeram, G. Mukherjee, and S. Manna, Small-world properties of the indian railway network. Physical Review E 67, No 3 (2003), 036106.10.1103/PhysRevE.67.036106Suche in Google Scholar

[43] D. Sornette and V. Pisarenko, Fractal plate tectonics. Geophysical Research Letters 30, No 3 (2003), 1105.10.1029/2002GL015043Suche in Google Scholar

[44] S. Stein, M. Liu, E. Calais, and Q. Li, Mid-continent earthquakes as a complex system. Seismological Research Letters 80, No 4 (2009), 551-553.Suche in Google Scholar

[45] S. H. Strogatz, Exploring complex networks. Nature 410, No 6825 (2001), 268-276.Suche in Google Scholar

[46] J. Tenreiro Machado, Accessing complexity from genome information. Communications in Nonlinear Science and Numerical Simulation 17, No 6 (2012), 2237-2243.Suche in Google Scholar

[47] J. Tenreiro Machado and A. M. Lopes, Dynamical analysis of the global warming. Mathematical Problems in Engineering 2012 (2012), Article ID 971641 (12 p).10.1155/2012/971641Suche in Google Scholar

[48] J. Tenreiro Machado and A. M. Lopes, The persistence of memory. Nonlinear Dynamics, Online first (Aug. 2014); DOI 10.1007/s11071-014-1645-1.10.1007/s11071-014-1645-1Suche in Google Scholar

[49] D. L. Turcotte and B. D. Malamud, 14 earthquakes as a complex system. International Geophysics 81, Part A (2002), 209-227, IV.10.1016/S0074-6142(02)80217-0Suche in Google Scholar

[50] J. Wang, Optimized scale-free networks against cascading failures. International J. of Modern Physics C 23, No 11 (2012), 1250075 (12p).10.1142/S0129183112500751Suche in Google Scholar

[51] Z. Wu, L. A. Braunstein, V. Colizza, R. Cohen, S. Havlin, and H. E. Stanley, Optimal paths in complex networks with correlated weights: The worldwide airport network. Physical Review E 74, No 5 (2006), 056104.10.1103/PhysRevE.74.056104Suche in Google Scholar PubMed

[52] W.-B. Zhang, Theory of complex systems and economic dynamics. Nonlinear Dynamics, Psychology, and Life Sciences 6, No 2 (2002), 83-101.Suche in Google Scholar

[53] C. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag, and J. Kurths, Hierarchical organization unveiled by functional connectivity in complex brain networks. Physical Review Letters 97, No 23 (2006), 238103. 10.1103/PhysRevLett.97.238103Suche in Google Scholar PubMed

Received: 2014-9-16
Published Online: 2015-3-13
Published in Print: 2015-4-1

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Heruntergeladen am 16.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/fca-2015-0029/pdf
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