Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation
Comptes Rendus de l'Académie des Sciences - Series III - Sciences de la Vie - Tập 324 - Trang 773-793 - 2001
Tài liệu tham khảo
Prigogine, 1980
Laplace, 1814
Korn, 1987, Regulation and significance of probabilistic release mechanisms at central synapses
Korn, 1991, Quantal analysis and synaptic efficacy in the cns, Trends Neurosci., 14, 439, 10.1016/0166-2236(91)90042-S
Poincaré, 1908
Bergé, 1998
Hindmarsh, 1984, A model of neuronal bursting using three coupled first order differential equations, Proc. R. Soc. Lond., 221, 87, 10.1098/rspb.1984.0024
Glass, 1988
Ruelle, 1991
Lorenz, 1963, Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130, 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
May, 1974, Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos, Science, 186, 645, 10.1126/science.186.4164.645
May, 1976, Simple mathematical models with very complicated dynamics, Nature, 261, 459, 10.1038/261459a0
Ruelle, 1971, On the nature of turbulence, Comm. Math. Phys., 20, 167, 10.1007/BF01646553
Takens, 1981, Lecture Notes in Mathematics, Vol. 898
Feigenbaum, 1978, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys., 19, 25, 10.1007/BF01020332
Li, 1975, Period three implies chaos, Am. Math. Monthly, 82, 985, 10.2307/2318254
Diner, 1992, Les voies du chaos déterministe dans l'école russe
Kellert, 1993
Rapp, 1993, Chaos in the neurosciences: Cautionary tales from the frontier, Biologist, 40, 89
Kaplan, 1995
Devaney, 1986
Ambegaokar, 1996
Feigenbaum, 1980, Universal behaviour in nonlinear systems, Los Alamos Science, 1, 4
Hilborn, 1994
Bak, 1996, How nature works?
Schroeder, 1991
Eckmann, 1985, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys., 57, 617, 10.1103/RevModPhys.57.617
Shannon, 1949
Kantz, 1997
Lorenz, 1993
Schreiber, 1999, Interdisciplinary application of nonlinear time series methods, Phys. Rep., 308, 1, 10.1016/S0370-1573(98)00035-0
Packard, 1980, Geometry from a time series, Phys. Rev. Lett., 45, 712, 10.1103/PhysRevLett.45.712
Sauer, 1994, Reconstruction of dynamical systems from interspike intervals, Phys. Rev. Lett., 72, 3811, 10.1103/PhysRevLett.72.3811
Grassberger, 1991, Nonlinear time series analysis, Int. J. Bif. Chaos, 1, 521, 10.1142/S0218127491000403
Glass, 1998, Chaos in Neural Systems
Eckmann, 1987, Recurrence plots of dynamical systems, Euro- phys. Lett., 1, 973, 10.1209/0295-5075/4/9/004
Faure, 1997, A nonrandom dynamic component in the synaptic noise of a central neuron, Proc. Natl. Sci. USA, 94, 6506, 10.1073/pnas.94.12.6506
Webber, 1994, Dynamical assessment of physiological systems and states using recurrence plot strategies, Am. J. Physiol., 965
Trulla, 1996, Recurrence quantification analysis of the logistic equation with transcients, Phys. Lett. A, 223, 255, 10.1016/S0375-9601(96)00741-4
Faure, 1998, A new method to estimate the kolmogorov entropy on recurrence plots: its application to neuronal signals, Physica D, 122, 265, 10.1016/S0167-2789(98)00177-8
Gao, 2000, On the structures and quantification of recurrence plots, Phys. Lett. A, 270, 75, 10.1016/S0375-9601(00)00304-2
Grassberger, 1983, Characterization of strange attractors, Phys. Rev. Lett., 50, 346, 10.1103/PhysRevLett.50.346
Provenzale, 1992, Distinguishing between low-dimensional dynamics and randomness in measured time series, Physica D, 58, 31, 10.1016/0167-2789(92)90100-2
Aihara, 1982, Temporally coherent organization and instabilities in squid giant axons, J. Theor. Biol., 95, 697, 10.1016/0022-5193(82)90349-6
Hayashi, 1992, Chaotic nature of bursting discharges in the onchidium pacemaker neuron, J. Theor. Biol., 156, 269, 10.1016/S0022-5193(05)80676-9
Abarbanel, 1996
Faure, 2000, Probabilistic release and the transmission of complex firing patterns between neurons, J. Neurophysiol., 84, 3010, 10.1152/jn.2000.84.6.3010
Ehlers, 1998, Low doses of ethanol reduce evidence for nonlinear structure in brain activity, J. Neurosci., 18, 7474, 10.1523/JNEUROSCI.18-18-07474.1998
Theiler, 1988, Lacunarity in a best estimator of fractal dimension, Phys. Lett. A, 133, 195, 10.1016/0375-9601(88)91016-X
Pincus, 1991, Approximate entropy as a measure of system complexity, Proc. Natl. Acad. Sci. USA, 88, 2297, 10.1073/pnas.88.6.2297
Prichard, 1995, Generalized redundancies for time series analysis, Physica D, 84, 476, 10.1016/0167-2789(95)00041-2
Palus, 1995, Testing for nonlinearity using redundancies: Quantitative and qualitative aspects, Physica D, 80, 186, 10.1016/0167-2789(95)90079-9
Lorenz, 1969, Atmospheric predictability as revealed by naturally occurring analogues, J. Atmos. Sci., 2, 636, 10.1175/1520-0469(1969)26<636:APARBN>2.0.CO;2
Casdagli, 1992
Sugihara, 1990, Nonlinear forecasting as a way of distinguishing chaos from measurement errors in time series, Nature, 344, 734, 10.1038/344734a0
Sauer, 1993, Time series prediction by using delay coordinate embedding
Chang, 1994, Stochastic versus deterministic variability in simple neuronal circuits: I. monosynaptic spinal cord reflexes, Biophys. J., 67, 671, 10.1016/S0006-3495(94)80526-0
Richardson, 1998, Encoding chaos in neural spike trains, Phys. Rev. Lett., 80, 2485, 10.1103/PhysRevLett.80.2485
Auerbach, 1987, Exploring chaotic motion through periodic orbits, Phys. Rev. Lett., 58, 2387, 10.1103/PhysRevLett.58.2387
Cvitanovic, 1988, Invariant measurement of strange sets in terms of cycles, Phys. Rev. Lett., 61, 2729, 10.1103/PhysRevLett.61.2729
So, 1998, Periodic orbits: A new language for neuronal nynamics, Biophys. J., 74, 2776, 10.1016/S0006-3495(98)77985-8
Kaplan, 1999, Finding and characterizing unstable fixed points by controlling system dynamics
Pei, 1996, Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor, Nature, 379, 618, 10.1038/379618a0
Crutchfield, 1989, Inferring statistical complexity, Phys. Rev. Lett., 63, 105, 10.1103/PhysRevLett.63.105
Rapp, 1994, The algorithmic complexity of neural spike trains increases during focal seizures, J. Neurosci., 14, 4731, 10.1523/JNEUROSCI.14-08-04731.1994
Chaïtin, 1975, Randomness and mathematical proof, Sci. Am., 232, 47, 10.1038/scientificamerican0575-47
Beltrami, 1999
Ford, 1987, Directions in classical chaos
Ford, 1989, What is chaos, that we should be mindful of it?
Sinai, 1992, L'aléatoire du non-aléatoire. Article initialement paru en russe dans Priroda (La Nature) 3 (1981) 72
Theiler, 1992, Testing for nonlinearity in time series: the method of surrogate data, Physica D, 58, 77, 10.1016/0167-2789(92)90102-S
Rapp, 1994, Phase randomized surrogates can produce spurious identifications of non random structure, Physics letters A, 192, 27, 10.1016/0375-9601(94)91010-3
Rapp, Surrogate data pathologies and the false-positive rejection of the null hypothesis, Int. J. Bifurcation Chaos
Schreiber, 1996, Improved surrogate data for nonlinearity tests, Phys. Rev. Lett., 77, 635, 10.1103/PhysRevLett.77.635
Schreiber, 2000, Surrogate time series, Physica D, 142, 346, 10.1016/S0167-2789(00)00043-9
Mackey, 1977, Oscillation and chaos in physiological control systems, Science, 197, 287, 10.1126/science.267326
Ott, 1990, Controlling chaos, Phys. Rev. Lett., 64, 1196, 10.1103/PhysRevLett.64.1196
Petrov, 1993, Controlling chaos in the belousov-zhabotinsky reaction, Nature, 361, 240, 10.1038/361240a0
Shinbrot, 1993, Using small perturbations to control chaos, Nature, 363, 411, 10.1038/363411a0
Ditto, 1995, Techniques for the control of chaos, Physica D, 86, 198, 10.1016/0167-2789(95)00101-9
Ott, 1995, Controlling chaos, Physics Today, 34, 10.1063/1.881461
Auerbach, 1992, Controlling chaos in high dimensional systems, Phys. Rev. Lett., 69, 3479, 10.1103/PhysRevLett.69.3479
Boccaletti, 2000, The control of chaos: theory and applications, Physics Reports, 329, 103, 10.1016/S0370-1573(99)00096-4
Garfinkel, 1992, Controlling cardiac chaos, Science, 257, 1230, 10.1126/science.1519060
Schiff, 1994, Controlling chaos in the brain, Nature, 8, 615, 10.1038/370615a0
Mackey, 1987, Dynamical diseases, Ann. N. Y. Acad. Sci., 504, 16, 10.1111/j.1749-6632.1987.tb48723.x