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Volumn 56, Issue 1-2, 2009, Pages 23-44

Nonlinear dynamics and chaos methods in neurodynamics and complex data analysis

Author keywords

Computational neuroscience; Medical diagnosis; Nonlinear dynamics and chaos

Indexed keywords

CHAOS THEORY; COMPUTATIONAL METHODS; DATA STRUCTURES; DIAGNOSIS; DIFFERENTIAL EQUATIONS; DYNAMICS; ENTROPY; MEDICAL APPLICATIONS; NEURAL NETWORKS; ROBOTICS; ROBOTS; TELECOMMUNICATION NETWORKS; TIME SERIES; TIME SERIES ANALYSIS;

EID: 61449202019     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-008-9376-9     Document Type: Article
Times cited : (49)

References (70)
  • 1
    • 0017713690 scopus 로고
    • Dynamics of pattern formation in lateral-inhibition type neural fields
    • S. Amari 1977 Dynamics of pattern formation in lateral-inhibition type neural fields Biol. Cybern. 27 77 87
    • (1977) Biol. Cybern. , vol.27 , pp. 77-87
    • Amari, S.1
  • 3
    • 0001463465 scopus 로고
    • Statistical description of chaotic attractors
    • R. Badii A. Politi 1985 Statistical description of chaotic attractors J. Stat. Phys. 40 725
    • (1985) J. Stat. Phys. , vol.40 , pp. 725
    • Badii, R.1    Politi, A.2
  • 5
    • 48549109620 scopus 로고
    • Power law behaviour of Lyapunov exponents in some conservative dynamical systems
    • G. Benettin 1984 Power law behaviour of Lyapunov exponents in some conservative dynamical systems Physica D 13 211 213
    • (1984) Physica D , vol.13 , pp. 211-213
    • Benettin, G.1
  • 6
    • 0018989294 scopus 로고
    • Lyapunov exponents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them. Part 1: Theory, and Part 2: Numerical applications
    • G. Benettin A. Giorgilli L. Galgani J.M. Strelcyn 1980 Lyapunov exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: Theory, and Part 2: Numerical applications Meccanica 15 9 30
    • (1980) Meccanica , vol.15 , pp. 9-30
    • Benettin, G.1    Giorgilli, A.2    Galgani, L.3    Strelcyn, J.M.4
  • 9
    • 0000685770 scopus 로고    scopus 로고
    • Geometry of dynamics, Lyapunov exponents, and phase transitions
    • L. Caiani L. Casetti C. Clementi M. Pettini 1997 Geometry of dynamics, Lyapunov exponents, and phase transitions Phys. Rev. Lett. 79 4361 4364
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 4361-4364
    • Caiani, L.1    Casetti, L.2    Clementi, C.3    Pettini, M.4
  • 11
    • 0012097571 scopus 로고
    • A universal instability of many-dimensional oscillator systems
    • B.V. Chirikov 1979 A universal instability of many-dimensional oscillator systems Phys. Rep. 52 264 379
    • (1979) Phys. Rep. , vol.52 , pp. 264-379
    • Chirikov, B.V.1
  • 12
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • J.P. Eckmann D. Ruelle 1985 Ergodic theory of chaos and strange attractors Rev. Mod. Phys. 57 617
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617
    • Eckmann, J.P.1    Ruelle, D.2
  • 13
    • 0001631767 scopus 로고
    • Dynamical trajectories and geodesics
    • L.P. Eisenhart 1929 Dynamical trajectories and geodesics Math. Ann. 30 591 606
    • (1929) Math. Ann. , vol.30 , pp. 591-606
    • Eisenhart, L.P.1
  • 14
    • 0019443177 scopus 로고
    • The behavior of rings of coupled oscillators
    • G.B. Ermentrout 1981 The behavior of rings of coupled oscillators J. Math. Biol. 12 327
    • (1981) J. Math. Biol. , vol.12 , pp. 327
    • Ermentrout, G.B.1
  • 15
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • R.A. FitzHugh 1961 Impulses and physiological states in theoretical models of nerve membrane Biophys J. 1 445 466
    • (1961) Biophys J. , vol.1 , pp. 445-466
    • Fitzhugh, R.A.1
  • 16
    • 0002721581 scopus 로고
    • Mathematical models of excitation and propagation in nerve
    • McGraw-Hill New York
    • FitzHugh, R.A.: Mathematical models of excitation and propagation in nerve. In: Schwan, H.P. (ed.) Biological Engineering. McGraw-Hill, New York (1969)
    • (1969) Biological Engineering
    • Fitzhugh, R.A.1    Schwan, H.P.2
  • 17
    • 0001013648 scopus 로고    scopus 로고
    • Topological aspects of geometrical signatures of phase transitions
    • R. Franzosi L. Casetti L. Spinelli M. Pettini 1999 Topological aspects of geometrical signatures of phase transitions Phys. Rev. E 60 5009
    • (1999) Phys. Rev. e , vol.60 , pp. 5009
    • Franzosi, R.1    Casetti, L.2    Spinelli, L.3    Pettini, M.4
  • 18
    • 4644230094 scopus 로고    scopus 로고
    • Theorem on the origin of phase transitions
    • 6
    • R. Franzosi M. Pettini 2004 Theorem on the origin of phase transitions Phys. Rev. Lett. 92 6 060601
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 060601
    • Franzosi, R.1    Pettini, M.2
  • 19
    • 4243588056 scopus 로고    scopus 로고
    • Topology and phase transitions: A paradigmatic evidence
    • R. Franzosi M. Pettini L. Spinelli 2000 Topology and phase transitions: a paradigmatic evidence Phys. Rev. Lett. 84 2774 2777
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 2774-2777
    • Franzosi, R.1    Pettini, M.2    Spinelli, L.3
  • 20
    • 0000090102 scopus 로고
    • Finite sample corrections to entropy and dimension estimates
    • P. Grassberger 1988 Finite sample corrections to entropy and dimension estimates Phys. Lett. A 128 369
    • (1988) Phys. Lett. A , vol.128 , pp. 369
    • Grassberger, P.1
  • 21
    • 61449205138 scopus 로고    scopus 로고
    • Context-sensitive generation of goal-directed behavioral sequences based on neural attractor dynamics
    • Munich, Germany, May
    • Grote, C., Schöner, G.: Context-sensitive generation of goal-directed behavioral sequences based on neural attractor dynamics. In: Proceedings of the ISR/ROBOTIK2006 Joint Conference on Robotics, Munich, Germany, May (2006)
    • (2006) Proceedings of the ISR/ROBOTIK2006 Joint Conference on Robotics
    • Grote, C.1
  • 25
    • 0000810560 scopus 로고    scopus 로고
    • Practical implementation of nonlinear time series methods: The TISEAN package
    • R. Hegger H. Kantz T. Schreiber 1999 Practical implementation of nonlinear time series methods: The TISEAN package Chaos 9 413
    • (1999) Chaos , vol.9 , pp. 413
    • Hegger, R.1    Kantz, H.2    Schreiber, T.3
  • 27
    • 0030762575 scopus 로고    scopus 로고
    • Predicting survival in heart failure case control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics
    • K.K.L. Ho 1997 Predicting survival in heart failure case control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics Circulation 96 842 848
    • (1997) Circulation , vol.96 , pp. 842-848
    • Ho, K.K.L.1
  • 28
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and application to conduction and excitation in nerve
    • A.L. Hodgkin A.F. Huxley 1952 A quantitative description of membrane current and application to conduction and excitation in nerve J. Physiol. 117 500 544
    • (1952) J. Physiol. , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 39
    • 0032667738 scopus 로고    scopus 로고
    • Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models
    • E.M. Izhikevich 1999 Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models IEEE Trans. Neu. Netw. 10 499 507
    • (1999) IEEE Trans. Neu. Netw. , vol.10 , pp. 499-507
    • Izhikevich, E.M.1
  • 40
    • 0034767817 scopus 로고    scopus 로고
    • Resonate-and-fire neurons
    • E.M. Izhikevich 2001 Resonate-and-fire neurons Neu. Netw. 14 883 894
    • (2001) Neu. Netw. , vol.14 , pp. 883-894
    • Izhikevich, E.M.1
  • 41
    • 4344661328 scopus 로고    scopus 로고
    • Which model to use for cortical spiking neurons? IEEE Trans
    • E.M. Izhikevich 2004 Which model to use for cortical spiking neurons? IEEE Trans Neu. Netw. 15 1063 1070
    • (2004) Neu. Netw. , vol.15 , pp. 1063-1070
    • Izhikevich, E.M.1
  • 42
    • 0001870258 scopus 로고
    • A robust method to estimate the maximal Lyapunov exponent of a time series
    • H. Kantz 1994 A robust method to estimate the maximal Lyapunov exponent of a time series Phys. Lett. A 185 77
    • (1994) Phys. Lett. A , vol.185 , pp. 77
    • Kantz, H.1
  • 46
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E.N. Lorenz 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130 141
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 47
    • 0031029949 scopus 로고    scopus 로고
    • Nonlinear deterministic analysis of tissue texture: A stereological study on mastopatic and mammary cancer tissue using chaos theory
    • 1
    • T. Mattfeldt 1997 Nonlinear deterministic analysis of tissue texture: a stereological study on mastopatic and mammary cancer tissue using chaos theory J. Microsc. 185 1 47 66
    • (1997) J. Microsc. , vol.185 , pp. 47-66
    • Mattfeldt, T.1
  • 48
    • 0019405994 scopus 로고
    • Voltage oscillations in the barnacle giant muscle fiber
    • C. Morris H. Lecar 1981 Voltage oscillations in the barnacle giant muscle fiber Biophys. J. 35 193 213
    • (1981) Biophys. J. , vol.35 , pp. 193-213
    • Morris, C.1    Lecar, H.2
  • 49
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating 1214-nerve axons
    • J. Nagumo S. Arimoto S. Yoshizawa 1960 An active pulse transmission line simulating 1214-nerve axons Proc. IRL 50 2061 2070
    • (1960) Proc. IRL , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 52
    • 30844431754 scopus 로고    scopus 로고
    • Visualization of synchronization of the uterine contraction signals: Running cross-correlation and wavelet running cross-correlation methods
    • E. Oczeretko J. Swiatecka A. Kitlas T. Laudanski P. Pierzynski 2006 Visualization of synchronization of the uterine contraction signals: Running cross-correlation and wavelet running cross-correlation methods Med. Eng. Phys. 28 75 81
    • (2006) Med. Eng. Phys. , vol.28 , pp. 75-81
    • Oczeretko, E.1    Swiatecka, J.2    Kitlas, A.3    Laudanski, T.4    Pierzynski, P.5
  • 54
  • 55
    • 34548014750 scopus 로고    scopus 로고
    • New research models and novel signal analysis in studies on preterm labor: A key to progress?
    • Suppl. 1
    • P. Pierzynski E. Oczeretko P. Laudanski T. Laudanski 2007 New research models and novel signal analysis in studies on preterm labor: a key to progress? BMC Pregnancy Childbirth 7 Suppl. 1 S6
    • (2007) BMC Pregnancy Childbirth , vol.7 , pp. 6
    • Pierzynski, P.1    Oczeretko, E.2    Laudanski, P.3    Laudanski, T.4
  • 56
    • 0344995288 scopus 로고    scopus 로고
    • Cardiac interbeat interval dynamics from childhood to senescence: Comparison of conventional and new measures based on fractals and chaos
    • S.M. Pikkujamsa 1999 Cardiac interbeat interval dynamics from childhood to senescence: Comparison of conventional and new measures based on fractals and chaos Circulation 100 393 399
    • (1999) Circulation , vol.100 , pp. 393-399
    • Pikkujamsa, S.M.1
  • 57
    • 0001263361 scopus 로고
    • Approximate entropy (ApEn) as a complexity measure
    • S. Pincus 1995 Approximate entropy (ApEn) as a complexity measure Chaos 5 110 117
    • (1995) Chaos , vol.5 , pp. 110-117
    • Pincus, S.1
  • 60
    • 43949166788 scopus 로고
    • A practical method for calculating largest Lyapunov exponents from small data sets
    • M.T. Rosenstein J.J. Collins C.J. De Luca 1993 A practical method for calculating largest Lyapunov exponents from small data sets Physica D 65 117
    • (1993) Physica D , vol.65 , pp. 117
    • Rosenstein, M.T.1    Collins, J.J.2    De Luca, C.J.3
  • 61
    • 21344485017 scopus 로고
    • How many delay coordinates do you need?
    • T. Sauer J. Yorke 1993 How many delay coordinates do you need? Int. J. Bifurc. Chaos 3 737
    • (1993) Int. J. Bifurc. Chaos , vol.3 , pp. 737
    • Sauer, T.1    Yorke, J.2
  • 62
    • 0026976153 scopus 로고
    • A dynamical systems approach to task-level system integration used to plan and control autonomous vehicle motion
    • G. Schöner M. Dose 1992 A dynamical systems approach to task-level system integration used to plan and control autonomous vehicle motion Robotics Autom. Syst. 10 253 267
    • (1992) Robotics Autom. Syst. , vol.10 , pp. 253-267
    • Schöner, G.1    Dose, M.2
  • 63
    • 0029539342 scopus 로고
    • Dynamics of behavior: Theory and applications for autonomous robot architectures
    • G. Schöner M. Dose C. Engels 1995 Dynamics of behavior: theory and applications for autonomous robot architectures Robotics Autom. Syst. 16 213 245
    • (1995) Robotics Autom. Syst. , vol.16 , pp. 213-245
    • Schöner, G.1    Dose, M.2    Engels, C.3
  • 65
    • 16344384708 scopus 로고    scopus 로고
    • Normal and pathological oscillatory communication in the brain
    • A. Schnitzler J. Gross 2005 Normal and pathological oscillatory communication in the brain Nat. Rev. Neurosci. 6 285 296
    • (2005) Nat. Rev. Neurosci. , vol.6 , pp. 285-296
    • Schnitzler, A.1    Gross, J.2
  • 66
    • 33244465600 scopus 로고    scopus 로고
    • An exploratory study of chaos in human-machine system dynamics
    • 2
    • S. Sharma 2006 An exploratory study of chaos in human-machine system dynamics IEEE Trans. Syst. Man Cybern. B 36 2 319 326
    • (2006) IEEE Trans. Syst. Man Cybern. B , vol.36 , pp. 319-326
    • Sharma, S.1
  • 68
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • S.H. Strogatz 2000 From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators Physica D 143 1 20
    • (2000) Physica D , vol.143 , pp. 1-20
    • Strogatz, S.H.1
  • 70
    • 0015260274 scopus 로고
    • Excitatory and inhibitory interactions in localized populations of model neurons
    • H.R. Wilson J.D. Cowan 1972 Excitatory and inhibitory interactions in localized populations of model neurons Biophys. J. 12 1 24
    • (1972) Biophys. J. , vol.12 , pp. 1-24
    • Wilson, H.R.1    Cowan, J.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.