메뉴 건너뛰기




Volumn 9, Issue 9, 2014, Pages

Distinguishing noise from chaos: Objective versus subjective criteria using horizontal visibility graph

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; CHAOTIC DYNAMICS; CONFIDENCE INTERVAL; CORRELATION ANALYSIS; HORIZONTAL VISIBILITY GRAPH; INFORMATION SCIENCE; KERNEL METHOD; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; METHODOLOGY; NOISE; STATISTICAL ANALYSIS; TIME SERIES ANALYSIS; WHITE NOISE; BIOLOGY; NONLINEAR SYSTEM; STATISTICS;

EID: 84907478676     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0108004     Document Type: Article
Times cited : (89)

References (89)
  • 1
    • 33745216051 scopus 로고    scopus 로고
    • Complex network from pseudoperiodic time series: Topology versus dynamics
    • Zhang J, Small M (2006) Complex Network from Pseudoperiodic Time Series: Topology versus Dynamics. Phys. Rev. Letts., 96: 238701.
    • (2006) Phys. Rev. Letts. , vol.96 , pp. 238701
    • Zhang, J.1    Small, M.2
  • 2
    • 58149499440 scopus 로고    scopus 로고
    • Superfamily phenomena and motifs of networks induced from time series
    • Xu X, Zhang J, Small M (2008) Superfamily phenomena and motifs of networks induced from time series. Proc. Natl. Acad. Sci. USA 105: 19601-19605.
    • (2008) Proc. Natl. Acad. Sci. USA , vol.105 , pp. 19601-19605
    • Xu, X.1    Zhang, J.2    Small, M.3
  • 3
    • 84885148871 scopus 로고    scopus 로고
    • Recurrence networks from multivariate signals for uncovering dynamic transitions of horizontal oil-water stratified flows
    • Gao Z, Zhang X, Jin N, Donner RV, Marwan N, et al. (2013) Recurrence networks from multivariate signals for uncovering dynamic transitions of horizontal oil-water stratified flows. Europhysics Letters 103: 50004.
    • (2013) Europhysics Letters , vol.103 , pp. 50004
    • Gao, Z.1    Zhang, X.2    Jin, N.3    Donner, R.V.4    Marwan, N.5
  • 4
    • 53249147479 scopus 로고    scopus 로고
    • Characterizing pseudoperiodic time series through the complex network approach
    • Zhang J, Sun J, Luo X, Zhang K, Nakamura T, et al. (2008) Characterizing pseudoperiodic time series through the complex network approach. Physica D 237: 2856-2865.
    • (2008) Physica D , vol.237 , pp. 2856-2865
    • Zhang, J.1    Sun, J.2    Luo, X.3    Zhang, K.4    Nakamura, T.5
  • 6
    • 84885100071 scopus 로고    scopus 로고
    • Multivariate recurrence network analysis for characterizing horizontal oil-water two-phase flow
    • Gao ZK, Zhang X, Jin ND, Marwan N, Kurths J (2013) Multivariate recurrence network analysis for characterizing horizontal oil-water two-phase flow. Phys. Rev. E 88: 032910.
    • (2013) Phys. Rev. E , vol.88
    • Gao, Z.K.1    Zhang, X.2    Jin, N.D.3    Marwan, N.4    Kurths, J.5
  • 7
    • 5544310124 scopus 로고
    • Finite correlation dimension for stochastic systems with power-law spectra
    • Osborne AR, Provenzale A (1989) Finite correlation dimension for stochastic systems with power-law spectra. Physica D 35: 357-381.
    • (1989) Physica D , vol.35 , pp. 357-381
    • Osborne, A.R.1    Provenzale, A.2
  • 8
    • 0025199496 scopus 로고
    • Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
    • Sugihara G, May RM (1983) Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344: 734-741.
    • (1983) Nature , vol.344 , pp. 734-741
    • Sugihara, G.1    May, R.M.2
  • 9
    • 11944266815 scopus 로고
    • Direct test for determinism in a time series
    • Kaplan DT, Glass L (1992) Direct test for determinism in a time series. Phys. Rev. Lett. 68: 427-430.
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 427-430
    • Kaplan, D.T.1    Glass, L.2
  • 10
    • 0001594590 scopus 로고
    • Coarse-grained embeddings of time series: Random walks, Gaussian random processes, and deterministic chaos
    • Kaplan DT, Glass L (1993) Coarse-grained embeddings of time series: random walks, Gaussian random processes, and deterministic chaos. Physica D 64: 431-454.
    • (1993) Physica D , vol.64 , pp. 431-454
    • Kaplan, D.T.1    Glass, L.2
  • 11
    • 0033733522 scopus 로고    scopus 로고
    • Coarse grained dynamical entropies: Investigation of high-entropic dynamical systems
    • Kantz H, Olbrich E (2000) Coarse grained dynamical entropies: Investigation of high-entropic dynamical systems. Physica A 280: 34-48.
    • (2000) Physica A , vol.280 , pp. 34-48
    • Kantz, H.1    Olbrich, E.2
  • 13
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • Grasberger P, Procaccia I (1983) Characterization of Strange Attractors. Phys. Rev. Lett. 50: 346-349.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-349
    • Grasberger, P.1    Procaccia, I.2
  • 15
    • 0001450585 scopus 로고
    • A new metric invariant for transitive dynamical systems and automorphisms in lebesgue spaces
    • Kolmogorov AN (1959) A new metric invariant for transitive dynamical systems and automorphisms in Lebesgue spaces. Dokl. Akad. Nauk., USSR, 119: 861-864.
    • (1959) Dokl. Akad. Nauk., USSR , vol.119 , pp. 861-864
    • Kolmogorov, A.N.1
  • 16
    • 0000419815 scopus 로고
    • On the concept of entropy for a dynamical system
    • Sinai YG (1959) On the concept of entropy for a dynamical system. Dokl. Akad. Nauk., USSR, 124: 768-771.
    • (1959) Dokl. Akad. Nauk., USSR , vol.124 , pp. 768-771
    • Sinai, Y.G.1
  • 18
    • 80054043781 scopus 로고    scopus 로고
    • Causality and the entropy-complexity plane: Robustness and missing ordinal patters
    • Rosso OA, Carpi LC, Saco PM, Ravetti MG, Plastino A, et al. (2012) Causality and the entropy-complexity plane: robustness and missing ordinal patters. Physica A 391: 42-55.
    • (2012) Physica A , vol.391 , pp. 42-55
    • Rosso, O.A.1    Carpi, L.C.2    Saco, P.M.3    Ravetti, M.G.4    Plastino, A.5
  • 20
    • 84876819366 scopus 로고    scopus 로고
    • Characterization of chaotic maps using the permutation bandt-pompe probability distribution
    • Rosso OA, Olivares F, Zunino L, De Micco L, Aquino ALL, et al. (2013) Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution. Eur. Phys. J. B 86: 116-129.
    • (2013) Eur. Phys. J. B , vol.86 , pp. 116-129
    • Rosso, O.A.1    Olivares, F.2    Zunino, L.3    De Micco, L.4    Aquino, A.L.L.5
  • 21
    • 4243997063 scopus 로고    scopus 로고
    • Permutation entropy: A natural complexity measure for time series
    • Bandt C, Pompe B (2002) Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88: 174102.
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 174102
    • Bandt, C.1    Pompe, B.2
  • 22
    • 84867479144 scopus 로고    scopus 로고
    • Permutation entropy and its main biomedical and econophysics applications: A review
    • Zanin M, Zunino L, Rosso OA, Papo D (2012) Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review. Entropy 14: 1553-1577.
    • (2012) Entropy , vol.14 , pp. 1553-1577
    • Zanin, M.1    Zunino, L.2    Rosso, O.A.3    Papo, D.4
  • 23
    • 84856976575 scopus 로고    scopus 로고
    • Ambiguities in BandtPompe's methodology for local entropic quantifiers
    • Olivares F, Plastino A, Rosso OA (2012) Ambiguities in BandtPompe's methodology for local entropic quantifiers. Physica A 391: 2518-2526.
    • (2012) Physica A , vol.391 , pp. 2518-2526
    • Olivares, F.1    Plastino, A.2    Rosso, O.A.3
  • 24
    • 84859852632 scopus 로고    scopus 로고
    • Contrasting chaos with noise via local versus global information quantifiers
    • Olivares F, Plastino A, Rosso OA (2012) Contrasting chaos with noise via local versus global information quantifiers. Phys. Lett A 376: 1577-1583.
    • (2012) Phys. Lett A , vol.376 , pp. 1577-1583
    • Olivares, F.1    Plastino, A.2    Rosso, O.A.3
  • 26
    • 79051468958 scopus 로고    scopus 로고
    • True and false forbidden patterns in deterministic and random dynamics
    • Amigó JS, Zambrano S, Sanjuán MAF (2007) True and false forbidden patterns in deterministic and random dynamics. Europhys. Lett. 79: 50001.
    • (2007) Europhys. Lett. , vol.79 , pp. 50001
    • Amigó, J.S.1    Zambrano, S.2    Sanjuán, M.A.F.3
  • 27
    • 79051470683 scopus 로고    scopus 로고
    • Combinatorial detection of determinism in noisy time series
    • Amigó JM, Zambrano S, Sanjuán MAF (2008) Combinatorial detection of determinism in noisy time series. Europhys. Lett. 83: 60005.
    • (2008) Europhys. Lett. , vol.83 , pp. 60005
    • Amigó, J.M.1    Zambrano, S.2    Sanjuán, M.A.F.3
  • 29
    • 77649276052 scopus 로고    scopus 로고
    • Missing ordinal patterns in correlated noises
    • Carpi LC, Saco PM, Rosso OA (2010) Missing ordinal patterns in correlated noises. Physica A 389: 2020-2029.
    • (2010) Physica A , vol.389 , pp. 2020-2029
    • Carpi, L.C.1    Saco, P.M.2    Rosso, O.A.3
  • 31
    • 0001571275 scopus 로고
    • An attractor in a solar time series
    • Kurths J, Herzel H (1987) An attractor in a solar time series. Physica D 25: 165-172.
    • (1987) Physica D , vol.25 , pp. 165-172
    • Kurths, J.1    Herzel, H.2
  • 34
    • 80052530600 scopus 로고    scopus 로고
    • Feigenbaun graphs: A complex network perspective of chaos
    • Luque B, Lacasa L, Ballesteros FJ, Robledo A (2011) Feigenbaun graphs: A complex network perspective of Chaos. PLoS ONE 6: e22411.
    • (2011) PLoS ONE , vol.6 , pp. e22411
    • Luque, B.1    Lacasa, L.2    Ballesteros, F.J.3    Robledo, A.4
  • 35
    • 84859329652 scopus 로고    scopus 로고
    • Analytical properties of horizontal visibility graphs in the feigenbaun scenario
    • Luque B, Lacasa L, Ballesteros FJ, Robledo A (2012) Analytical properties of horizontal visibility graphs in the Feigenbaun scenario. Chaos 22: 013109.
    • (2012) Chaos , vol.22
    • Luque, B.1    Lacasa, L.2    Ballesteros, F.J.3    Robledo, A.4
  • 36
    • 78651338617 scopus 로고    scopus 로고
    • Description of stochastic and chaotic series using visibility graphs
    • Lacasa L, Toral R (2010) Description of stochastic and chaotic series using visibility graphs. Phys. Rev. E. 82: 036120.
    • (2010) Phys. Rev. E. , vol.82
    • Lacasa, L.1    Toral, R.2
  • 37
    • 70350043594 scopus 로고    scopus 로고
    • Horizontal visibility graphs: Exact results for random time series
    • Luque B, Lacasa L, Ballesteros F, Luque J (2009) Horizontal visibility graphs: exact results for random time series. Phys. Rev. E 80: 046103.
    • (2009) Phys. Rev. E , vol.80
    • Luque, B.1    Lacasa, L.2    Ballesteros, F.3    Luque, J.4
  • 38
    • 85003908875 scopus 로고    scopus 로고
    • Chaos and time series analysis
    • Sprott JC (2012) Chaos and Time series analysis. Complex Systems 21: 193-200.
    • (2012) Complex Systems , vol.21 , pp. 193-200
    • Sprott, J.C.1
  • 40
    • 0017185443 scopus 로고
    • Simple mathematical models with very complicated dynamics
    • May R (1976) Simple mathematical models with very complicated dynamics. Nature 261: 45-67.
    • (1976) Nature , vol.261 , pp. 45-67
    • May, R.1
  • 44
    • 57849103363 scopus 로고
    • Symbolic description of periodic windows in the antisymmetric cubic map
    • Zeng W, Ding M, Li J (1985) Symbolic description of periodic windows in the antisymmetric cubic map. Chinese Physics Letters 2: 293-296.
    • (1985) Chinese Physics Letters , vol.2 , pp. 293-296
    • Zeng, W.1    Ding, M.2    Li, J.3
  • 48
    • 0141671267 scopus 로고    scopus 로고
    • Robust chaos in neural networks
    • Potapov A, Ali MK (2000) Robust chaos in neural networks. Phys. Lett. A 277: 310-322.
    • (2000) Phys. Lett. A , vol.277 , pp. 310-322
    • Potapov, A.1    Ali, M.K.2
  • 49
    • 0009520409 scopus 로고
    • Strange attractors, chaotic behaviour, and information flow
    • Shaw R (1981) Strange attractors, chaotic behaviour, and information flow. Zeitschrift für Naturforschung A 36: 80-112.
    • (1981) Zeitschrift für Naturforschung A , vol.36 , pp. 80-112
    • Shaw, R.1
  • 50
    • 0000071902 scopus 로고
    • Small denominators, I: Mappings of the circumference into itself
    • Arnold VI (1965) Small denominators, I: mappings of the circumference into itself. American Mathematical Society Translation Series 46: 213-284.
    • (1965) American Mathematical Society Translation Series , vol.46 , pp. 213-284
    • Arnold, V.I.1
  • 51
    • 0002591468 scopus 로고
    • A two-dimensional mapping with a strange attractor
    • Hénon M (1976) A two-dimensional mapping with a strange attractor. Communication on Mathematical Physics 50: 69-77.
    • (1976) Communication on Mathematical Physics , vol.50 , pp. 69-77
    • Hénon, M.1
  • 52
    • 0002634180 scopus 로고
    • Un attracteur étrange? Du type attracteur de Hénon
    • Lozi R (1978) Un attracteur étrange? Du type attracteur de Hénon. Journal de Physique 39, 9-10.
    • (1978) Journal de Physique , vol.39 , pp. 9-10
    • Lozi, R.1
  • 53
    • 0000009552 scopus 로고
    • Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computerassisted study
    • Aronson DG, Chory MA, Hall GR, McGehee RP (1982) Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computerassisted study. Communications in Mathematical Physics 83: 304-354.
    • (1982) Communications in Mathematical Physics , vol.83 , pp. 304-354
    • Aronson, D.G.1    Chory, M.A.2    Hall, G.R.3    McGehee, R.P.4
  • 55
    • 0005232238 scopus 로고
    • A chaotic mapping that displays its own homoclinic structure
    • Whitehead RR, Macdonald N (1984) A chaotic mapping that displays its own homoclinic structure. Physica D 13: 401-407.
    • (1984) Physica D , vol.13 , pp. 401-407
    • Whitehead, R.R.1    Macdonald, N.2
  • 57
  • 58
    • 0018508810 scopus 로고
    • Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system
    • Ikeda E (1979) Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Optics Communications 30: 257-61.
    • (1979) Optics Communications , vol.30 , pp. 257-261
    • Ikeda, E.1
  • 59
  • 60
    • 0016740371 scopus 로고
    • Dynamic complexity in predadorprey models framed in difference equations
    • Beddington JR, Free CA, Lawton JH (1975) Dynamic complexity in predadorprey models framed in difference equations. Nature 255: 58-60.
    • (1975) Nature , vol.255 , pp. 58-60
    • Beddington, J.R.1    Free, C.A.2    Lawton, J.H.3
  • 61
    • 0012097571 scopus 로고
    • A universal instability of many-dimensional oscillator systems
    • Chirikov BV (1979) A universal instability of many-dimensional oscillator systems. Physics Reports 52: 273-379.
    • (1979) Physics Reports , vol.52 , pp. 273-379
    • Chirikov, B.V.1
  • 62
    • 0001039322 scopus 로고
    • Numerical study of quadratic area-preserving mappings
    • Hénon M (1969) Numerical study of quadratic area-preserving mappings. Quarterly of Applied Mathematics 27: 291-312.
    • (1969) Quarterly of Applied Mathematics , vol.27 , pp. 291-312
    • Hénon, M.1
  • 64
    • 0010678168 scopus 로고
    • A piecewise linear model for the zones of instability of an area-preserving map
    • Devaney RL (1984) A piecewise linear model for the zones of instability of an area-preserving map. Physica D 10: 387-93.
    • (1984) Physica D , vol.10 , pp. 387-393
    • Devaney, R.L.1
  • 66
    • 0004154108 scopus 로고
    • Seattle, USA: University of Washington Press
    • Lorenz EN (1993) The essence of chaos. Seattle, USA: University of Washington Press.
    • (1993) The Essence of Chaos
    • Lorenz, E.N.1
  • 67
    • 26544461279 scopus 로고
    • Reconstruction expansion as geometry based framework for choosing proper delay times
    • Rosenstein MT, Collins JJ, De Luca CJ (1994) Reconstruction expansion as geometry based framework for choosing proper delay times. Physica D 73: 82-98.
    • (1994) Physica D , vol.73 , pp. 82-98
    • Rosenstein, M.T.1    Collins, J.J.2    De Luca, C.J.3
  • 69
    • 84867753937 scopus 로고    scopus 로고
    • Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach
    • Zunino L, Soriano M, Rosso OA (2012) Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach. Phys. Rev. E 86: 046210.
    • (2012) Phys. Rev. E , vol.86
    • Zunino, L.1    Soriano, M.2    Rosso, O.A.3
  • 71
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flows
    • Lorenz EN (1963) Deterministic nonperiodic flows. J. Atmos. Sci. 20: 130-141.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 72
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rössler OE (1976) An equation for continuous chaos. Phys. Lett. A 57: 397-398.
    • (1976) Phys. Lett. A , vol.57 , pp. 397-398
    • Rössler, O.E.1
  • 74
    • 84876876549 scopus 로고    scopus 로고
    • Available Accessed: 2014 May 7
    • Larrondo HA (2012) Matlab program: noisefk.m, Available: http://www.mathworks.com/matlabcentral/fileexchange/35381. Accessed: 2014 May 7.
    • (2012) Matlab Program: Noisefk.m
    • Larrondo, H.A.1
  • 76
    • 33847322599 scopus 로고    scopus 로고
    • Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools
    • Zunino L, Pérez DG, Martín MT, Plastino A, Garavaglia M, et al. (2007) Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools. Phys. Rev. E 75: (2007) 021115.
    • (2007) Phys. Rev. E , vol.75 , Issue.2007
    • Zunino, L.1    Pérez, D.G.2    Martín, M.T.3    Plastino, A.4    Garavaglia, M.5
  • 77
    • 0000481680 scopus 로고    scopus 로고
    • The wavelet-based synthesis for the fractional brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation
    • Abry P, Sellan F (1996) The wavelet-based synthesis for the fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation. Applied and Computational Harmonic Analysis 3: 377-383.
    • (1996) Applied and Computational Harmonic Analysis , vol.3 , pp. 377-383
    • Abry, P.1    Sellan, F.2
  • 79
    • 80955178306 scopus 로고    scopus 로고
    • Horizontal visibility graphs transformed from fractional brownian motions: Topological properties versus the hurst index
    • Xie W, Zhou W (2013) Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index. Physica A 390: 3592-3601.
    • (2013) Physica A , vol.390 , pp. 3592-3601
    • Xie, W.1    Zhou, W.2
  • 81
    • 0037737627 scopus 로고    scopus 로고
    • Analysis of signals in the fisher-shannon information plane
    • Vignat C, Bercher JF (2003) Analysis of signals in the Fisher-Shannon information plane. Phys. Lett. A. 312: 27-33.
    • (2003) Phys. Lett. A , vol.312 , pp. 27-33
    • Vignat, C.1    Bercher, J.F.2
  • 82
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • 623-656
    • Shannon CE (1948) A mathematical theory of communication. Bell Syst. Technol. J. 27: 379-423, 623-56.
    • (1948) Bell Syst. Technol. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 83
    • 0001735517 scopus 로고
    • On the mathematical foundations of theoretical statistics
    • Fisher RA (1922) On the mathematical foundations of theoretical statistics. Philos. Trans. R. Soc. Lond. Ser. A 222: 309-368.
    • (1922) Philos. Trans. R. Soc. Lond. Ser. A , vol.222 , pp. 309-368
    • Fisher, R.A.1
  • 86
    • 84988122246 scopus 로고
    • Discrete approximations to the csiszár, renyi, and fisher measures of information
    • Zografos K, Ferentinos K, Papaioannou T (1986) Discrete approximations to the Csiszár, Renyi, and Fisher measures of information. Canad. J. Stat. 14: 355-366.
    • (1986) Canad. J. Stat. , vol.14 , pp. 355-366
    • Zografos, K.1    Ferentinos, K.2    Papaioannou, T.3
  • 87
    • 0347032951 scopus 로고
    • Discretization problems on generalized entropies and R-divergences
    • Pardo L, Morales D, Ferentinos K, Zografos K (1994) Discretization problems on generalized entropies and R-divergences. Kybernetika 30: 445-460.
    • (1994) Kybernetika , vol.30 , pp. 445-460
    • Pardo, L.1    Morales, D.2    Ferentinos, K.3    Zografos, K.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.