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IDENTIFICATION OF COMPLEX PROCESSES BASED ON ANALYSIS OF PHASE SPACE STRUCTURES

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Abstract

The problem of investigation of temporal and/or spatial behavior of highly nonlinear or complex natural systems has long been of fundamental scientific interest. At the same time it is presently well understood that identification of dynamics of processes in complex natural systems, through their qualitative description and quantitative evaluation, is far from a purely academic question and has an essential practical importance. This is quite understandable as systems with complex dynamics abound in nature and examples can be found in very different areas such as medicine and biology (rhythms, physiological cycles, epidemics), atmosphere (climate and weather change), geophysics (tides, earthquakes, volcanoes, magnetic field variations), economy (financial markets behavior, exchange rates), engineering (friction, fracturing), communication (electronic networks, internet packet dynamics) etc. The past two decades of research on qualitative and especially quantitative investigations of dynamics of real processes of different origin brought significant progress in the understanding of behavior of natural processes. At the same time serious drawbacks have also been revealed.

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References

  • Abarbanel, H.D.I., Brown, R., Sidorowich., and Tsimring, L. S. (1993) The Analysis of Observed Chaotic Data in Physical Systems, Rev. Mod. Phys. 65 (4), 1331–1392.

    Article  MathSciNet  Google Scholar 

  • Antani, J.A., Wayne, H.H., and Kuzman, W.J. (1979) Ejaction Phase Indexes by Invasive and Noninvasive Methods: An Apexcardiographic, Echocardiographic and Ventriculographyc Correlative Study, Am. J. Cardiol. 43(2), 239–247.

    Article  Google Scholar 

  • Arecchi, F.T., and Fariny, A. (1996) Lexicon of Complexity, ABS. Sest. F. Firenze.

    Google Scholar 

  • Argyris, J. H., Faust, G., and Haase, M. (1994) An Exploration of Chaos, North-Holland, Amsterdam.

    MATH  Google Scholar 

  • Bak, P., Tang, C., and Wiesenfeld, K. (1988) Self-organized Criticality, Phys. Rev. A 38, 364–374.

    Article  MathSciNet  Google Scholar 

  • Beeler, N.M. and Lockner, D.A. (2003) Why Earthquakes Correlate Weakly with the SolidEarth Tides: Effects of Periodic Stress on the Rate and Probability of Earthquake Occurrence, J. Geophys. Res., ESE. 108(8), 1–17.

    Google Scholar 

  • Bennett, C. H. (1990) in Complexity, Entropy and the Physics of Information, ed., Addison-Wesley, Reading MA.

    Google Scholar 

  • Berge, P., Pomeau. Y., and Vidal, C. (1984) Order within Chaos, J. Wiley, NY.

    MATH  Google Scholar 

  • Bhattacharya, J. (1999) Search of Regularity in Irregular and Complex Signals, Nonlinear Dynamics PhD, Indian Institute of Technology, India.

    Google Scholar 

  • Boffetta, G., Cencini, M., Falcioni, M., and Vulpiani, A. (2002) Predictability: A Way to Characterize Complexity, Phys. Rep. 356, 367–474.

    Article  MATH  MathSciNet  Google Scholar 

  • Bowman D., Ouillon G., Sammis C., Sornette A., and Sornette, D. (1998) An Observational Test of the Critical Earthquake Concept, J. Geophys. Res. 103, 24359–24372.

    Article  Google Scholar 

  • Bunde, A., Kropp, J., and Schellnhuber H. J. (2002) The Science of Disasters, Climate Disruptions, Heart Attacks, Market Crashes, ed., Springer, Heidelberg.

    Google Scholar 

  • Casdagli, M.C. (1997) Recurrence Plots Revisited, Physica D 108, 12–44.

    Article  MATH  MathSciNet  Google Scholar 

  • Castro, R. and Sauer, T. (1997) Correlation Dimension of Attractors through Interspike Interval, Phys. Rev. E 55(1), 287–290.

    Article  Google Scholar 

  • Chelidze, T. and Matcharashvili, T. (2003) Electromagnetic Control of Earthquakes Dynamics? Computers and Geosciences 29(5), 587–593.

    Article  Google Scholar 

  • Chelidze, T., Matcharashvili, T., Gogiashvili, J., Lursmanashvili, O., and Devidze, M. (2005) Phase Synchronization of Slip in Laboratory Slider System, Nonlin. Proc. in Geophysics 12, 1–8.

    Google Scholar 

  • Cover T. M. and Thomas, J. A. (1991) Elements of Information Theory, Wiley, New York.

    MATH  Google Scholar 

  • Eckman, J.P. and Ruelle, D. (1985) Ergodic Theory of Chaos and Strange Attractors, Rev. Mod. Phys. 57(3), 617–656.

    Article  Google Scholar 

  • Elbert, T., Ray, W.J., Kowalik, Z.J., Skinner, J.E., Graf, E. K., and Birnbauer, N. (1994) Chaos and Physiology, Physiol Rev. 74, 1–49.

    Google Scholar 

  • Garfinkel, A., Chen, P., Walter, D.O., Karaguezian, H., Kogan, B., Evans, S.J., Karpoukhin, M., Hwang, C., Uchida, T., Gotoh, M., and Weiss, J.N. (1997) Qoasiperiodicity and Chaos in Cardiac Fibrillation, J. Clin. Invest. 99(2), 305–314.

    Article  Google Scholar 

  • Gavrilenko, P., Melikadze, G., Chelidze, T., Gibert, D., and Kumsiashvili, G. (2000) Permanent Water Level Drop Associated with Spitak Earthquake: Observations at Lisi Borehole and Modeling, Geophys. J. Int. 143, 83–98.

    Article  Google Scholar 

  • Geller, R.J. (1999) Earthquake Prediction: Is this Debate Necessary? Nature, Macmillan Publishers Ltd.; http://helix.nature.com.

    Google Scholar 

  • Gilmore, R. (1993) A New Test for Chaos, J. Econ. Behav. Organization 22, 209–237.

    Article  Google Scholar 

  • Gilmore, R. (1998) Topological Analysis of Chaotic Dynamical Systems, Rev. Mod. Phys. 70, 1455–1529.

    Article  MathSciNet  Google Scholar 

  • Goltz C. (1998) Fractal and Chaotic Properties of Earthquakes, Springer, Berlin.

    Google Scholar 

  • Govindan, R.B., Narayanan, K., and Gopinathan, M.S. (1998) On the Evidence of Deterministic Chaos in ECG: Surrogate and Predictability Analysis, Chaos 8(2), 495–502.

    Article  MATH  Google Scholar 

  • Grassberger, P. and Procaccia, I. (1983) Estimation of the Kolmogorov Entropy from a Chaotic Signal, Phys. Rev. A 28(4), 2591–2593.

    Article  Google Scholar 

  • Hegger, R., Kantz, H., and Schreiber, T. (1999) Practical Implementation of Nonlinear Time Series Methods: The TISEAN Package, Chaos 9, 413–440.

    Article  MATH  Google Scholar 

  • Hodgson G. M. (1993) Economics and Evolution: Bringing Life Back into Economics, Ann Arbor: University of Michigan Press.

    Google Scholar 

  • Ivanski, J. and Bradley, E. (1998) Recurrence Plots of Experimental Data: To Embed or not to Embed? Chaos 8, 861.

    Article  Google Scholar 

  • Johansen. A. and Sornette, D. (1999) Acoustic Radiation Controls Dynamic Friction: Evidence from a Spring-Block Experiment, Phys. Rev. Lett. 82, 5152–5155.

    Article  Google Scholar 

  • Jones, N. (2001) The Quake Machine, New Scientist 30(6), 34–37.

    Google Scholar 

  • Kagan, Y.Y. (1994) Observational Evidence for Earthquakes as a Nonlinear Dynamic Process, Physica D 77, 160–192.

    Article  Google Scholar 

  • Kagan, Y.Y. (1997) Are Earthquakes Predictable? Geophys. J. Int. 131, 505–525.

    Article  Google Scholar 

  • Kanamori, H. and Brodsky, E.E. (2001) The Physics of Earthquakes, Physics Today 6, 34–40.

    Article  Google Scholar 

  • Kantz, H. and Schreiber, T. (1997) Nonlinear Time Series Analysis, Cambridge, University Press.

    MATH  Google Scholar 

  • Keilis-Borok, V.I. (1994) Symptoms of Instability in a System of Earthquake-Prone Faults, Physica D 77, 193–199.

    Article  Google Scholar 

  • Kennel, M.B., Brown R., and Abarbanel, H.D.I. (1992) Determining Minimum Embedding Dimension using a Geometrical Construction, Phys. Rev. A 45, 3403–3411.

    Article  Google Scholar 

  • King, C. Y., Azuma, S., Igarashi, G., Ohno, M., Saito, H., and Wakita, H. (1999) Earthquake–Related Water-lewel Changes at 16 Closely Clustered Wells in Tono, Central Japan, J. Geoph. Res. 104(6), 13073–13082.

    Article  Google Scholar 

  • Knopoff, L. (1999) Earthquake Prediction is Difficult But Not Impossible, Nature, Macmillan Publ. Ltd.; http://helix.nature.com.

    Google Scholar 

  • Korvin, G. (1992) Fractal Models in the Earth Sciences, Elsevier, NY.

    Google Scholar 

  • Kraskov, A., Stogbauer, H., and Grassberger, P. (2004) Estimating Mutual Information, Phys. Rev. 69 (066138).

    Google Scholar 

  • Kumpel, H. (1994) Evidence for Self-similarity in the Harmonic Development of Earth Tides, In: Fractals and Dynamic Systems in Geoscience, Kruhl, J. H. ed., Springer, Berlin, pp. 213–220.

    Google Scholar 

  • Lefebvre, J.H., Goodings, D.A., Kamath., and Fallen, E.L. (1993) Predictability of Normal Heart Rhytms and Deterministic Chaos, Chaos 3(2), 267–276.

    Article  Google Scholar 

  • Main, I. (1997) Earthquakes–Long Odds on Prediction, Nature 385, 19–20.

    Article  Google Scholar 

  • Marzochi, W. (1996) Detecting Low-dimensional Chaos in Time Series of Finite Length Generated from Discrete Parameter Processes, Physica D 90, 31–39.

    Article  Google Scholar 

  • Marwan, M., Wessel, N., Meyerfeldt, U., Schirdewan, A., and Kurths, J. (2002) Recurrence-plot-based Measures of Complexity and their Application to Heart-rate-variability Data, Phys. Rev. E 66 (026702).

    Google Scholar 

  • Marwan, M. (2003) Encounters with neighborhood, University of Potsdam, Germany, Theoretical Physics PhD.

    Google Scholar 

  • Mason, D. T., Spenn, J.F., and Zelis, R. (1970) Quantification of the Contractile State of the Intact Human Heart, Am. J. Cardiol 26(3), 248–257.

    Article  Google Scholar 

  • Matcharashvili, T., Chelidze, T., and Javakhishvili, Z. (2000) Nonlinear Analysis of Magnitude and Interevent Time Interval Sequences for Earthquakes of Caucasian Region, Nonlinear Processes in Geophysics 7, 9–19.

    Google Scholar 

  • Matcharashvili, T. and Janiashvili, M. (2001) Investigation of Variability of Indexes of Myocardial Contractility by Complexity Measure in Patients with Hypertension, In Sulis W., Trofimova I. (Eds) Proceedings of the NATO ASI Nonlinear dynamics in life and social sciences, 204–214, IOS Press, Amsterdam.

    Google Scholar 

  • Matcharashvili, T., Chelidze, T., Javakhishvili Z., and Ghlonti, E. (2002) Detecting Differences in Dynamics of Small Earthquakes Temporal Distribution before And After Large Events, Computers & Geosciences 28(5), 693–700.

    Article  Google Scholar 

  • McCauley, J. L. (2004) Dynamics of Markets: Econophysics and Finance. Cambridge, UK, Cambridge University Press.

    MATH  Google Scholar 

  • Ott, E. (1993) Chaos in Dynamical Systems, Cambridge University Press.

    Google Scholar 

  • Packard, N.H., Crutchfield, J.P., Farmer, J.D., and Shaw, R.S. (1980) Geometry from a Time Series, Phys. Rev. Lett. 45, 712–716.

    Article  Google Scholar 

  • Peinke, J., Matcharashvili, T., Chelidze, T., Gogiashvili, J., Nawroth, A., Lursmanashvili, O., and Javakhishvili, Z. (2006) Influence of Periodic Variations in Water Level on Regional Seismic Activity Around a Large Reservoir, Field and Laboratory Model, Physics of the Earth and Planetary Interior 156(2), 130–142.

    Article  Google Scholar 

  • Pikkujamsa, S., Makikallio, T., Sourander, L., Raiha., I., Puukka, P., Skytta, J, Peng, C.K., Goldberger, A., and Huikuri, H. (2006) Cardiac Interbeat Interval Dinamics from Childhood to Senescence: Comparison of Conventional and New Measures Based on Fractals and Chaos Theory, Circulation 100, 383–393.

    Google Scholar 

  • Pikovsky, A., Rosenblum, M.G., and Kurth. J. (2003) Synchronization: Universal Concept in Nonlinear Science, Cambridge University Press 411.

    Google Scholar 

  • Rapp, P.E., Albano, A.M., Schmah, T.I., and Farwell, L. A. (1993) Filtered Noise can Mimic Low-dimensional Chaotic Attractors, Phys. Rev. E. 47(4), 2289–2297.

    Article  Google Scholar 

  • Rapp, P.E., Albano, A.M., Zimmerman, I. D., and Jumenez-Montero, M.A. (1994) Phase-randomized Surrogates Can Produce Spurious Identification of Non-random Structure, Phys. Lett. A 192(1), 27–33.

    Article  Google Scholar 

  • Rapp, P. E., Cellucci, C. J., Korslund, K. E., Watanabe, T. A., and Jimenez-Montano, M. A. (2001) Effective Normalization of Complexity Measurements for Epoch Length and Sampling Frequency, Phys. Rev. 64 (016209).

    Google Scholar 

  • Rombouts, S.A., Keunen, R.W., and Stam, C.J. (1995) Investigation of Nonlinear Structure in Multichannel EEG, Phys.Lett. A 202(5/6), 352–358.

    Article  Google Scholar 

  • Rosenstein, M. T., Collins, J. J., and DeLuca, C. J. (1993) A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets, Physica D 65, 117–134.

    Article  MATH  MathSciNet  Google Scholar 

  • Ruelle, D. (1994) Ehere Can One Hope to Profitably Apply the Ideas of Chaos? Physics Today 47(7), 24–32.

    Google Scholar 

  • Rundle, J., Turcotte, D., and Klein, W. (2000) GeoComplexity and the Physics of Earthquakes, AGU, Washington.

    Google Scholar 

  • Sato, S., Sano, M., and Sawada, Y. (1987) Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in High Dimensional Chaotic Systems, Prog. Theor. Phys. 77, 1–5.

    Article  MathSciNet  Google Scholar 

  • Scholz C.H. (1990) Earthquakes as Chaos, Nature 348, 197–198.

    Article  Google Scholar 

  • Schreiber, T. (1993) Extremely Simple Nonlinear Noise-reduction Method, Phys. Rev. E 47(4), 2401–2404.

    Article  MathSciNet  Google Scholar 

  • Schreiber, T. (1999) Interdisciplinary Application of Nonlinear Time Series Methods, Phys. Rep. 308, 1–64.

    Article  MathSciNet  Google Scholar 

  • Schreiber, T., and Schmitz, A. (1999) Testing for Nonlinearity in Unevenly Sampled Time Series, Phys. Rev. E 59(044).

    Google Scholar 

  • Shannon, C. E. (1948) A Mathematical Theory of Communications, The Bell System, Techn. J. 27, 623–656.

    MathSciNet  Google Scholar 

  • Shannon, C. E. (1964) The Mathematical Theory of Communication, University of Illinois, Urbana, IL.

    Google Scholar 

  • Shiner, J. S., Davison, M., and Landsberg, P. T. (1999) Simple Measure for Complexity, Phys. Rev. E 59(2), 1459–1464.

    Article  Google Scholar 

  • Sibson, R. (1994) Simple Measure for Complexity, In: Geofluids: Origin, Migration and Evolution of Fluids in sedimentary Basins, Parnell J., ed., The Geological Society, London, pp. 69–84.

    Google Scholar 

  • Simpson, D.W., Leith, W. S., and Scholz. C. (1988) Two Types of Reservoir-induced Seismicity, Bull. Seism. Soc. Am. 78, 2025–2040.

    Google Scholar 

  • Sivakumar, B., Berndtsson, R., Olsson, J., and Jinno, K. (2002) Reply to “Which Chaos in the Rainfall-runoff Process”, Hydrol. Sci. J. 47(1), 149–58.

    Article  Google Scholar 

  • Smirnov, V.B. (1995) Fractal Properties of Seismicity of Caucasus, J. of Earthq. Prediction Res. 4, 31–45.

    Google Scholar 

  • Sprott, J. C. and Rowlands, G. (1995) Chaos Data Analyzer; the Professional Version, AIP, NY.

    Google Scholar 

  • Takens, F. (1981) Detecting Strange Attractors in Fluid Turbulence, In: Dynamical Systems and Turbulence, Rand, D., and Young, L.S., ed., Berlin, pp. 366–381.

    Google Scholar 

  • Talwani, P. (1997) On Nature of Reservoir-induced Seismicity, Pure and Appl. Geophys. 150, 473–492.

    Article  Google Scholar 

  • Tarasov, N.T. (1997) Crustal Seismicity Variation Under Electric Action, Transactions (Doklady) of the Russian Academy of Sciences 353(3), 445–448.

    MathSciNet  Google Scholar 

  • Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J.D. (1992) Testing for Nonlinearity in Time Series: The Method of Surrogate Data, Physica D 58, 77–94.

    Article  Google Scholar 

  • Theiler, J. and Prichard, D. (1997) Using “Surrogate-surrogate Data” to Calibrate the Actual Rate of False Positives in Tests for Nonlinearity in Time Series, In: Nonlinear Dynamics and Time Series, Cutler, D., and Kaplan, D.T., ed., Fields Institute Communications, pp. 99–113.

    Google Scholar 

  • Turcotte, D. (1992) Fractals and Chaos in Geology and Geophysics, Thesis PhD, University Press, Cambridge.

    Google Scholar 

  • Vidale, J.E., Agnew, D.C., Johnston, M.J.S., and Oppenheimer, D.H. (1998) Absence of Earthquake Correlation with Earth Tides: An Indication of High Preseismic Fault Stress Rate, J. Geophys. Res. 103(24), 567–572.

    Google Scholar 

  • Volykhin, A.M., Bragin, V.D., and Zubovich, A.P. (1993) Geodynamic Processes in Geophysical Fields, Moscow, Nauka.

    Google Scholar 

  • Wackerbauer, R., Witt, A., Atmanspacher, H., Kurths, J., and Scheingraber, H. (1994) A Comparative Classification of Complexity Measures, Chaos, Solitons & Fractals 4, 133–137.

    Article  MATH  MathSciNet  Google Scholar 

  • Weiss, J.N., Garfinkel, A., Karaguezian, H., Zhilin, Q., and Chen, P. (1999) Chaos and Transition to Ventricular Fibrilation: A New Approach to Antiarrhythmic Drug Evaluation, Circulation 99(21), 2819–2826.

    Google Scholar 

  • Wolf, A., Swift, J., Swinney, H., and Vastano, J. (1985) Determining Lyapunov Exponents from a Time Series, Physica D 16, 285–317.

    Article  MATH  MathSciNet  Google Scholar 

  • Wyss, M. (1997) Cannot Earthquakes Be Predicted? Science 278, 487–488.

    Article  Google Scholar 

  • Yang, P., Brasseur, G. P., Gille, J. C., and Madronich, S. (1994) Dimensionalities of Ozone Attractors and their Global Distribution, Physica D 76 (3310343).

    Google Scholar 

  • Yao, W., Essex, C., Yu, P., and Davison, M. (2004) Measure of Predictability, Phys. Rev. E 69, 110–123.

    Article  MathSciNet  Google Scholar 

  • Zbilut, J.P. and Weber, C. L. (1992) Embeddings and Delays as Derived from Quantification of Recurrence Plots, Phys. Lett. A 171, 199–203.

    Article  Google Scholar 

  • Zbilut, J.P.A., Giuliani, C.L., and Webber Jr. (1998) Detecting Deterministic Signals in Exceptionally Noisy Environments Using Cross-recurrence Quantification, Phys. Lett. A 246, 122–128.

    Article  Google Scholar 

  • Zhang, X. and Thakor, N.V. (1999) Detecting Ventricular Tachicardia and Fibrillation by Complexity Measure, IEEE Trans. on Biomed. Eng. 46(5), 548–555.

    Article  Google Scholar 

  • Zokhowski. M., Winkowska-Nowak, K., and Nowak, A. (1997) Autocorrelation of R-R Distributions as a Measure of Heart Variability, Phys. Rev. E 56(3), 3725–3727.

    Article  Google Scholar 

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Matcharashvili, T., Chelidze, T., Janiashvili, M. (2007). IDENTIFICATION OF COMPLEX PROCESSES BASED ON ANALYSIS OF PHASE SPACE STRUCTURES. In: Byrnes, J. (eds) Imaging for Detection and Identification. NATO Security through Science Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5620-8_11

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