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Masoller, C.; Rosso, O.A. "Quantifying the complexity of the delayed logistic map" (2011) Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 369(1935):425-438
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Abstract:

Statistical complexity measures are used to quantify the degree of complexity of the delayed logistic map, with linear and nonlinear feedback. We employ two methods for calculating the complexity measures, one with the 'histogram-based' probability distribution function and the other one with ordinal patterns. We show that these methods provide complementary information about the complexity of the delay-induced dynamics: there are parameter regions where the histogram-based complexity is zero while the ordinal pattern complexity is not, and vice versa. We also show that the time series generated from the nonlinear delayed logistic map can present zero missing or forbidden patterns, i.e. all possible ordinal patterns are realized into orbits. This journal is © 2011 The Royal Society.

Registro:

Documento: Artículo
Título:Quantifying the complexity of the delayed logistic map
Autor:Masoller, C.; Rosso, O.A.
Filiación:Departament de Física i Enginyeria Nuclear, Escola Tecnica Superior d'Enginyeries Industrial i Aeronautica de Terrassa, Universitat Politècnica de Catalunya, Colom 11, 08222 Terrassa, Barcelona, Spain
Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627-Campus Pampulha. C.P. 702, 30123-970, Belo Horizonte, MG, Brazil
Chaos and Biology Group, Instituto de Cálculo, Universidad de Buenos Aires, 1428 Ciudad Universitaria, Buenos Aires, Argentina
Palabras clave:Complexity; Nonlinear dynamics; Time-delayed systems; Time-series analysis; Distribution functions; Dynamics; Graphic methods; Harmonic analysis; Nonlinear feedback; Time series; Complexity; Complexity measures; Degree of complexity; Forbidden pattern; Logistic maps; Non-linear dynamics; Ordinal pattern; Parameter regions; Statistical complexity; Time-delayed systems; Time series analysis
Año:2011
Volumen:369
Número:1935
Página de inicio:425
Página de fin:438
DOI: http://dx.doi.org/10.1098/rsta.2010.0281
Título revista:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Título revista abreviado:Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
ISSN:1364503X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1364503X_v369_n1935_p425_Masoller

Referencias:

  • Lugiato, L.A., Prati, F., Difference differential equations for a resonator with a very thin nonlinear medium (2010) Phys. Rev. Lett., 104, p. 233902. , doi:10.1103/PhysRevLett.104.233902
  • Stepan, G., Delay effects in brain dynamics (2009) Phil. Trans. R. Soc. A, 367, pp. 1059-1062. , doi:10.1098/rsta.2008.0279
  • Takeuchi, Y., Ma, W.B., Beretta, E., Global asymptotic properties of a delay SIR epidemic model with finite incubation times (2000) Nonlinear Anal. Theory Methods Appl., 42, pp. 931-947. , doi:10.1016/S0362-546X(99)00138-8
  • Wang, K.F., Wang, W.D., Pang, H.Y., Liu, X.N., Complex dynamic behaviour in a viral model with delayed immune response (2007) Physica D, 226, pp. 197-208. , doi:10.1016/j.physd.2006.12.001
  • Nagatani, T., The physics of traffic jams (2002) Rep. Prog. Phys., 65, pp. 1331-1386. , doi:10.1088/0034-4885/65/9/203
  • Foss, J., Longtin, A., Mensour, B., Milton, J., Multistability and delayed recurrent loops (1996) Phys. Rev. Lett., 76, pp. 708-711. , doi:10.1103/PhysRevLett.76.708
  • Foss, J., Moss, F., Milton, J., Noise, multistability, and delayed recurrent loops (1997) Phys. Rev. E, 55, pp. 4536-4543. , doi:10.1103/PhysRevE.55.4536
  • Ikeda, K., Matsumoto, K., High-dimensional chaotic behaviour in systems with timedelayed feedback (1987) Physica D, 29, pp. 223-235. , doi:10.1016/0167-2789(87)90058-3
  • Arecchi, F.T., Giacomelli, G., Lapucci, A., Meucci, R., 2-Dimensional representation of a delayed dynamic system (1992) Phys. Rev. A., 45, pp. R4225-R4228. , doi:10.1103/PhysRevA.45.R4225
  • Giacomelli, G., Meucci, R., Politi, A., Arecchi, F.T., Defects and space-like properties of delayed dynamical systems (1994) Phys. Rev. Lett., 73, pp. 1099-1102. , doi:10.1103/PhysRevLett.73.1099
  • Masoller, C., Spatio-temporal dynamics in the coherence collapsed regime of semiconductor lasers with optical feedback (1997) Chaos, 7, pp. 455-462. , doi:10.1063/1.166253
  • Ahlers, V., Parlitz, U., Lauterborn, W., Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers (1998) Phys. Rev. E, 58, pp. 7208-7213. , doi:10.1103/PhysRevE.58.7208
  • Feudel, U., Grebogi, C., Multistability and the control of complexity (1997) Chaos, 7, pp. 597-604. , doi:10.1063/1.166259
  • Lempel, A., Ziv, J., Complexity of finite sequences (1976) IEEE Trans. Inf. Theory, 22, pp. 75-81. , doi:10.1109/TIT.1976.1055501
  • Grassberger, P., Towards a quantitative theory of self-generated complexity (1986) Int. J. Theor. Phys., 25, p. 907. , doi:10.1007/BF00668821
  • Crutchfield, J.P., Young, K., Inferring statistical complexity (1989) Phys. Rev. Lett., 63, pp. 105-108. , doi:10.1103/PhysRevLett.63.105
  • Lopez-Ruiz, R., Mancini, H.L., Calbet, X., A statistical measure of complexity (1995) Phys. Lett. A, 209, pp. 321-326. , doi:10.1016/0375-9601(95)00867-5
  • Palus, M., Coarse-grained entropy rates for characterization of complex time series (1996) Physica D, 93, pp. 64-77. , doi:10.1016/0167-2789(95)00301-0
  • Shiner, J.S., Davison, M., Landsberg, P.T., Simple measure for complexity (1999) Phys. Rev. E, 59, pp. 1459-1464. , doi:10.1103/PhysRevE.59.1459
  • Bandt, C., Pompe, B., Permutation entropy: A natural complexity measure for time series (2002) Phys. Rev. Lett., 88, p. 174102. , doi:10.1103/PhysRevLett.88.174102
  • Boffetta, G., Cencini, M., Falcioni, M., Vulpiani, A., Predictability: A way to characterize complexity (2002) Phys. Rep., 356, pp. 367-474. , doi:10.1016/S0370-1573(01)00025-4
  • Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J., Recurrence-plotbased measures of complexity and their application to heart-rate-variability data (2002) Phys. Rev. E, 66, p. 026702. , doi:10.1103/PhysRevE.66.026702
  • Shalizi, C.R., Shalizi, K.L., Haslinger, R., Quantifying self-organization with optimal predictors (2004) Phys. Rev. Lett., 93, p. 118701. , doi:10.1103/PhysRevLett.93.118701
  • Martín, M.T., Plastino, A., Rosso, O.A., Generalized statistical complexity measures: Geometrical and analytical properties (2006) Physica A, 369, pp. 439-462. , doi:10.1016/j.physa.2005.11.053
  • Wolpert, D.H., MacReady, W., Using self-dissimilarity to quantify complexity (2007) Complexity, 12, pp. 77-85. , doi:10.1002/cplx.20165
  • Ke, D.G., Tong, Q.Y., Easily adaptable complexity measure for finite time series (2008) Phys. Rev. E, 77, p. 066215. , doi:10.1103/PhysRevE.77.066215
  • Cao, Y.H., Tung, W.W., Gao, J.B., Protopopescu, V.A., Hively, L.M., Detecting dynamical changes in time series using the permutation entropy (2004) Phys. Rev. E, 70, p. 046217. , doi:10.1103/PhysRevE.70.046217
  • Huang, H.Y., Lin, F.H., A speech feature extraction method using complexity measure for voice activity detection in WGN (2009) Speech Commun., 51, pp. 714-723. , doi:10.1016/j.specom.2009.02.004
  • Rosso, O.A., Larrondo, H.A., Martín, M.T., Plastino, A., Fuentes, M.A., Distinguishing noise from chaos (2007) Phys. Rev. Lett., 99, p. 154102. , doi:10.1103/PhysRevLett.99.154102
  • Rosso, O.A., Masoller, C., Detecting and quantifying stochastic and coherence resonances via information-theory complexity measurements (2009) Phys. Rev. E, 79, pp. 040106R. , doi:10.1103/PhysRevE.79.040106
  • Kaspar, F., Schuster, H.G., Easily calculable measure for the complexity of spatiotemporal patterns (1987) Phys. Rev. A, 36, pp. 842-848. , doi:10.1103/PhysRevA.36.842
  • Lindgren, K., Moore, C., Nordahl, M., Complexity of two-dimensional patterns (1998) J. Stat. Phys., 91, pp. 909-951. , doi:10.1023/A:1023027932419
  • Tononi, G., Sporns, O., Edelman, G.M., A measure for brain complexity-relating functional segregation and integration in the nervous-system (1994) Proc. Natl Acad. Sci. USA, 91, pp. 5033-5037. , doi:10.1073/pnas.91.11.5033
  • Barnett, L., Buckley, C.L., Bullock, S., Neural complexity and structural connectivity (2009) Phys. Rev. E, 79, p. 051914. , doi:10.1103/PhysRevE.79.051914
  • Angulo, J.C., Antolin, J., Atomic complexity measures in position and momentum spaces (2008) J. Chem. Phys., 128, p. 164109. , doi:10.1063/1.2907743
  • Dehesa, J.S., Lopez-Rosa, S., Manzano, D., Configuration complexities of hydrogenic atoms (2009) Eur. Phys. J. D, (55), pp. 539-548. , doi:10.1140/epjd/e2009-00251-1
  • Mazaheri, P., Shirazi, A.H., Saeedi, N., Jafari, G.R., Sahimi, M., Differentiating the protein coding and noncoding RNA segments of DNA using Shannon entropy (2010) Int. J. Mod. Phys. C, 21, pp. 1-9. , doi:10.1142/S0129183110014975
  • Wackerbauer, R., Witt, A., Altmanspacher, H., Kurths, J., Scheingraber, H., A comparative classification of complexity-measures (1994) Chaos Solitons Fractals, 4, pp. 133-173. , doi:10.1016/0960-0779(94)90023-X
  • Anteneodo, C., Plastino, A.R., Some features of the Lopez-Ruiz-Mancini-Calbet (LMC) statistical measure of complexity (1996) Phys. Lett. A, 223, pp. 348-354. , doi:10.1016/S0375-9601(96)00756-6
  • Martinez-Zerega, B.E., Pisarchik, A.N., Tsimring, L.S., Using periodic modulation to control coexisting attractors induced by delayed feedback (2003) Phys. Lett. A, 38, pp. 102-111. , doi:10.1016/j.physleta.2003.07.028
  • De Sousa Vieira, M., Lichtenberg, A.J., Controlling chaos using nonlinear feedback with delay (1996) Phys. Rev. E, 54, pp. 1200-1206. , doi:10.1103/PhysRevE.54.1200
  • Amigó, J.M., (2010) Permutation Complexity in Dynamical Systems: Ordinal Patterns, Permutation Entropy and All That, , Berlin, Germany: Springer
  • Kullback, S., Leibler, R.A., On information and sufficiency (1951) Ann. Math. Stat., 22, p. 79. , doi:10.1214/aoms/1177729694
  • Grandy Jr., W.T., Milonni, P.W., (1993) Physics and Probability: Essays in Honor of Edwin T. Jaynes, , New York, NY: Cambridge University Press
  • Amigó, J.M., Zambrano, S., Sanjuán, M.A.F., Combinatorial detection of determinism in noisy time series (2008) Europhys. Lett., 83, p. 60005. , doi:10.1209/0295-5075/83/60005
  • Amigó, J.M., Elizalde, S., Kennel, M., Forbidden patterns and shift systems (2008) J. Combin. Theory Ser. A, 115, pp. 485-504. , doi:10.1016/j.jcta.2007.07.004
  • Elizalde, S., Liu, Y., (2009) On Basic Forbidden Patterns of Functions, , http://arxiv.org/abs/0909.2277v1
  • Amigó, J.M., Zambrano, S., Sanjuán, M.A.F., True and false forbidden patterns in deterministic and random dynamics (2007) Europhys. Lett., 79, p. 50001. , doi:10.1209/0295-5075/79/50001
  • Farmer, J.D., Chaotic attractors of an infinite-dimensional dynamical system (1982) Physica D, 4, pp. 366-393. , doi:10.1016/0167-2789(82)90042-2
  • Le Berre, M., Ressayre, E., Tallet, A., Gibbs, H.M., High-dimension chaotic attractors of a nonlinear ring cavity (1986) Phys. Rev. Lett., 56, pp. 274-277. , doi:10.1103/PhysRevLett.56.274

Citas:

---------- APA ----------
Masoller, C. & Rosso, O.A. (2011) . Quantifying the complexity of the delayed logistic map. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369(1935), 425-438.
http://dx.doi.org/10.1098/rsta.2010.0281
---------- CHICAGO ----------
Masoller, C., Rosso, O.A. "Quantifying the complexity of the delayed logistic map" . Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1935 (2011) : 425-438.
http://dx.doi.org/10.1098/rsta.2010.0281
---------- MLA ----------
Masoller, C., Rosso, O.A. "Quantifying the complexity of the delayed logistic map" . Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 369, no. 1935, 2011, pp. 425-438.
http://dx.doi.org/10.1098/rsta.2010.0281
---------- VANCOUVER ----------
Masoller, C., Rosso, O.A. Quantifying the complexity of the delayed logistic map. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2011;369(1935):425-438.
http://dx.doi.org/10.1098/rsta.2010.0281