메뉴 건너뛰기




Volumn 112, Issue 10, 2002, Pages 1263-1284

Nonlinear interdependence in neural systems: Motivation, theory, and relevance

(2)  Breakspear, M a   Terry, J R a  

a NONE   (Australia)

Author keywords

Brain modeling; Cortical columns; Neural synchronization; Nonlinear dynamics

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; EFFERENT NERVE; ELECTROENCEPHALOGRAPHY; HUMAN; MOTONEURON; NERVE CELL; NERVE CELL NETWORK; NONLINEAR SYSTEM; PHYSIOLOGY; SENSORY NERVE CELL; SYSTEMS THEORY;

EID: 0036804631     PISSN: 00207454     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207450290026193     Document Type: Article
Times cited : (44)

References (60)
  • 1
    • 5544240364 scopus 로고
    • Blending chaotic attractors using the synchronization of chaos
    • Abarbanel, H., Rulkov, N., & Sushchik, M. (1995). Blending chaotic attractors using the synchronization of chaos. Physical Review E, 52, 214-217.
    • (1995) Physical Review E , vol.52 , pp. 214-217
    • Abarbanel, H.1    Rulkov, N.2    Sushchik, M.3
  • 2
    • 0000388249 scopus 로고    scopus 로고
    • Generalized synchronization of chaos: The auxiliary system approach
    • Abarbanel, H., Rulkov, N., & Sushchik, M. (1996). Generalized synchronization of chaos: The auxiliary system approach. Physical Review E, 53, 4528-4535.
    • (1996) Physical Review E , vol.53 , pp. 4528-4535
    • Abarbanel, H.1    Rulkov, N.2    Sushchik, M.3
  • 4
    • 0346401452 scopus 로고    scopus 로고
    • A robust method for detecting interdependencies: Application to intracranially recorded EEG
    • Arnhold, J., Grassberger, P., Lehnertz, K., & Elger, C. (1999). A robust method for detecting interdependencies: Application to intracranially recorded EEG. Physica D, 134, 419-430.
    • (1999) Physica D , vol.134 , pp. 419-430
    • Arnhold, J.1    Grassberger, P.2    Lehnertz, K.3    Elger, C.4
  • 5
    • 33744891845 scopus 로고
    • Bubbling of attractors and synchronization of chaotic attractors
    • Ashwin, P., Buescu, J., & Stewart, I. (1994). Bubbling of attractors and synchronization of chaotic attractors. Physics Letters A, 193, 126-139.
    • (1994) Physics Letters A , vol.193 , pp. 126-139
    • Ashwin, P.1    Buescu, J.2    Stewart, I.3
  • 6
    • 6144229366 scopus 로고    scopus 로고
    • From attractor to chaotic saddle: A tale of transverse stability
    • Ashwin P., Buescu, J., & Stewart, I. (1996). From attractor to chaotic saddle: A tale of transverse stability. Nonlinearity, 9, 703-737.
    • (1996) Nonlinearity , vol.9 , pp. 703-737
    • Ashwin, P.1    Buescu, J.2    Stewart, I.3
  • 8
    • 0000905680 scopus 로고    scopus 로고
    • Perception of odours by a nonlinear model of the olfactory bulb
    • Breakspear, M. (2001). Perception of odours by a nonlinear model of the olfactory bulb. International Journal of Neural Systems, 11, 101-124.
    • (2001) International Journal of Neural Systems , vol.11 , pp. 101-124
    • Breakspear, M.1
  • 9
    • 0036189086 scopus 로고    scopus 로고
    • Nonlinear phase desynchronization in human EEG
    • Breakspear, M. (2002). Nonlinear phase desynchronization in human EEG. Human Brain Mapping, 15, 175-198.
    • (2002) Human Brain Mapping , vol.15 , pp. 175-198
    • Breakspear, M.1
  • 10
    • 0036331380 scopus 로고    scopus 로고
    • Topographic organization of nonlinear interdependence in multichannel human EEG
    • Breakspear, M., & Terry, J. R. (2002a). Topographic organization of nonlinear interdependence in multichannel human EEG. NeuroImage, 14, 822-835.
    • (2002) NeuroImage , vol.14 , pp. 822-835
    • Breakspear, M.1    Terry, J.R.2
  • 11
    • 0036238798 scopus 로고    scopus 로고
    • Detection and description of nonlinear interdependence in normal multichannel human EEG
    • Breakspear, M., & Terry, J. R. (2002b). Detection and description of nonlinear interdependence in normal multichannel human EEG. Clinical Neurophysiology, 113, 735-753.
    • (2002) Clinical Neurophysiology , vol.113 , pp. 735-753
    • Breakspear, M.1    Terry, J.R.2
  • 14
    • 0035457757 scopus 로고    scopus 로고
    • Robust chaos in a model of the EEG: Implications for brain dynamics
    • Dafilis M. P., Liley D. T. J., & Cadusch P. J. (2001). Robust chaos in a model of the EEG: Implications for brain dynamics. Chaos, 11, 474-478.
    • (2001) Chaos , vol.11 , pp. 474-478
    • Dafilis, M.P.1    Liley, D.T.J.2    Cadusch, P.J.3
  • 15
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann J., & Ruelle D. (1985). Ergodic theory of chaos and strange attractors. Reviews of Modern Physics, 57, 617-656.
    • (1985) Reviews of Modern Physics , vol.57 , pp. 617-656
    • Eckmann, J.1    Ruelle, D.2
  • 16
    • 0040778278 scopus 로고    scopus 로고
    • Toward a comprehensive theory of brain activity: Coupled oscillators under external forces
    • Frank T., Daffertshofer A., Peper C., Beek, P., & Haken, H. (2000). Toward a comprehensive theory of brain activity: Coupled oscillators under external forces. Physica D, 144, 62-86.
    • (2000) Physica D , vol.144 , pp. 62-86
    • Frank, T.1    Daffertshofer, A.2    Peper, C.3    Beek, P.4    Haken, H.5
  • 18
    • 0002256723 scopus 로고
    • Stability theory of synchronized motion in coupled-oscillator system
    • Fujisaka, H., & Yamada, T. (1983). Stability theory of synchronized motion in coupled-oscillator system. Progress in Theoretical Physics, 69, 32-47.
    • (1983) Progress in Theoretical Physics , vol.69 , pp. 32-47
    • Fujisaka, H.1    Yamada, T.2
  • 19
    • 0033611002 scopus 로고    scopus 로고
    • Transitivity and blowout bifurcations in a class of globally coupled maps
    • Glendinning, P. (1999). Transitivity and blowout bifurcations in a class of globally coupled maps. Physics Letters A, 264, 303-310.
    • (1999) Physics Letters A , vol.264 , pp. 303-310
    • Glendinning, P.1
  • 20
    • 0024514737 scopus 로고
    • Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties
    • Gray, C., Konig, P., Engel, A., & Singer, W. (1989). Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Science, 338, 334-337.
    • (1989) Science , vol.338 , pp. 334-337
    • Gray, C.1    Konig, P.2    Engel, A.3    Singer, W.4
  • 22
    • 0031122644 scopus 로고    scopus 로고
    • Differentiable synchronization of chaos
    • Hunt, B., Ott, E., & Yorke, J. (1997). Differentiable synchronization of chaos. Physical Review E, 55, 4029-4034.
    • (1997) Physical Review E , vol.55 , pp. 4029-4034
    • Hunt, B.1    Ott, E.2    Yorke, J.3
  • 23
    • 0035359894 scopus 로고    scopus 로고
    • Synchronization of elliptic bursters
    • Izhikevich, E. (2001). Synchronization of elliptic bursters. SIAM Review, 43, 315-344.
    • (2001) SIAM Review , vol.43 , pp. 315-344
    • Izhikevich, E.1
  • 24
    • 0000456175 scopus 로고    scopus 로고
    • Field theory of electromagnetic brain activity
    • Jirsa, V. K., & Haken, H. (1996). Field theory of electromagnetic brain activity. Physical Review Letters, 77, 960-963.
    • (1996) Physical Review Letters , vol.77 , pp. 960-963
    • Jirsa, V.K.1    Haken, H.2
  • 25
    • 11744308383 scopus 로고    scopus 로고
    • Invariant manifolds and synchronization of coupled dynamical systems
    • Josic, K. (1998). Invariant manifolds and synchronization of coupled dynamical systems. Physical Review Letters, 80, 3053-3056.
    • (1998) Physical Review Letters , vol.80 , pp. 3053-3056
    • Josic, K.1
  • 26
    • 0000929946 scopus 로고    scopus 로고
    • Generalized synchronization, predictability and equivalence of unidirectionally coupled dynamical systems
    • Kocarev, L., & Parlitz, U. (1996). Generalized synchronization, predictability and equivalence of unidirectionally coupled dynamical systems. Physical Review Letters, 76, 816-1819.
    • (1996) Physical Review Letters , vol.76 , pp. 816-1819
    • Kocarev, L.1    Parlitz, U.2
  • 27
    • 0034169701 scopus 로고    scopus 로고
    • Robust synchronization of chaotic systems
    • Kocarev, L., Parlitz, U., & Brown, R. (2000). Robust synchronization of chaotic systems. Physical Review E, 61, 3716-3720.
    • (2000) Physical Review E , vol.61 , pp. 3716-3720
    • Kocarev, L.1    Parlitz, U.2    Brown, R.3
  • 29
    • 0033196391 scopus 로고    scopus 로고
    • A coupled ordinary differential equation lattice model for the simulation of epileptic seizures
    • Larter, R., & Speelman, B. (1999). A coupled ordinary differential equation lattice model for the simulation of epileptic seizures. Chaos, 9, 795-804.
    • (1999) Chaos , vol.9 , pp. 795-804
    • Larter, R.1    Speelman, B.2
  • 30
    • 0347662708 scopus 로고    scopus 로고
    • Nonlinear analyses of interictal EEG map the interdependencies in human focal epilepsy
    • LeVan Quyen, M., Martinerie, J., Adam, C., & Varela, F. (1999). Nonlinear analyses of interictal EEG map the interdependencies in human focal epilepsy. Physica D, 127, 250-266.
    • (1999) Physica D , vol.127 , pp. 250-266
    • LeVan Quyen, M.1    Martinerie, J.2    Adam, C.3    Varela, F.4
  • 32
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorenz, E. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Science, 20, 130-141.
    • (1963) Journal of Atmospheric Science , vol.20 , pp. 130-141
    • Lorenz, E.1
  • 33
    • 0030947940 scopus 로고    scopus 로고
    • Neural dynamics in a model of the thalamocortical system. I. Layers, loops and the emergence of fast synchronous oscillations
    • Lumer, E., Edelman, G., & Tononi, G. (1997). Neural dynamics in a model of the thalamocortical system. I. Layers, loops and the emergence of fast synchronous oscillations. Cerebral Cortex, 7, 207-227.
    • (1997) Cerebral Cortex , vol.7 , pp. 207-227
    • Lumer, E.1    Edelman, G.2    Tononi, G.3
  • 35
    • 4243958815 scopus 로고    scopus 로고
    • Transverse instability and riddled basins in a system of two coupled logistic maps
    • Maistrenko, Y., Maistrenko, V., Popovich, A., & Mosekilde, E. (1998). Transverse instability and riddled basins in a system of two coupled logistic maps. Physical Review E, 57, 2713-2724.
    • (1998) Physical Review E , vol.57 , pp. 2713-2724
    • Maistrenko, Y.1    Maistrenko, V.2    Popovich, A.3    Mosekilde, E.4
  • 36
    • 0031002495 scopus 로고    scopus 로고
    • The columnar organization of the neocortex
    • Mountcastle, V. B. (1997). The columnar organization of the neocortex. Brain, 120, 701-722.
    • (1997) Brain , vol.120 , pp. 701-722
    • Mountcastle, V.B.1
  • 37
  • 38
    • 0016251737 scopus 로고
    • The brain wave equation: A model for the EEG
    • Nunez, P. L. (1974). The brain wave equation: A model for the EEG. Mathematical Biosciences, 21, 279-297.
    • (1974) Mathematical Biosciences , vol.21 , pp. 279-297
    • Nunez, P.L.1
  • 40
    • 0343689904 scopus 로고
    • Synchronization in chaotic systems
    • Pecora, L., & Carroll, T. (1990). Synchronization in chaotic systems. Physical Review Letters, 64, 821-824.
    • (1990) Physical Review Letters , vol.64 , pp. 821-824
    • Pecora, L.1    Carroll, T.2
  • 41
    • 0001545699 scopus 로고    scopus 로고
    • Propagation and stability of waves of electrical activity in the cerebral cortex
    • Robinson, P. A., Rennie, C. J., & Wright, J. J. (1997). Propagation and stability of waves of electrical activity in the cerebral cortex. Physical Review E, 56, 826-840.
    • (1997) Physical Review E , vol.56 , pp. 826-840
    • Robinson, P.A.1    Rennie, C.J.2    Wright, J.J.3
  • 43
    • 85035247673 scopus 로고    scopus 로고
    • Dynamics of large-scale brain activity in normal arousal states and epileptic seizures
    • Robinson, P. A., Rennie, C. J., & Rowe, D. L. (2002). Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Physical Review E, 65, 041924.
    • (2002) Physical Review E , vol.65 , pp. 041924
    • Robinson, P.A.1    Rennie, C.J.2    Rowe, D.L.3
  • 45
    • 0031548743 scopus 로고    scopus 로고
    • From phase to lag synchronization in coupled chaotic oscillators
    • Rosenblum, M., Pikovsky, A., & Kurths, J. (1997). From phase to lag synchronization in coupled chaotic oscillators. Physical Review Letters, 78, 4193-4196.
    • (1997) Physical Review Letters , vol.78 , pp. 4193-4196
    • Rosenblum, M.1    Pikovsky, A.2    Kurths, J.3
  • 47
    • 33744833457 scopus 로고
    • Generalized synchronization of chaos in unidirectionally coupled chaotic systems
    • Rulkov, N., Sushchik, M., Tsimring, L., & Abarbenel, H. (1995). Generalized synchronization of chaos in unidirectionally coupled chaotic systems. Physical Review E, 51, 980-994.
    • (1995) Physical Review E , vol.51 , pp. 980-994
    • Rulkov, N.1    Sushchik, M.2    Tsimring, L.3    Abarbenel, H.4
  • 49
    • 0000528223 scopus 로고    scopus 로고
    • Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble
    • Schiff, S., So, P., Chang, T., Burke, R., & Sauer, T. (1997). Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. Physical Review E, 54, 6708-6724.
    • (1997) Physical Review E , vol.54 , pp. 6708-6724
    • Schiff, S.1    So, P.2    Chang, T.3    Burke, R.4    Sauer, T.5
  • 50
    • 0001860688 scopus 로고
    • Neuromodulations of neocortical dynamics
    • P. L. Nunez (Ed.). Oxford: Oxford University Press
    • Silberstein, R. B. (1995). Neuromodulations of neocortical dynamics. In P. L. Nunez (Ed.), Neocortical Dynamics and Human EEG Rhythms. Oxford: Oxford University Press.
    • (1995) Neocortical Dynamics and Human EEG Rhythms
    • Silberstein, R.B.1
  • 52
    • 85069104674 scopus 로고    scopus 로고
    • Synchronization of coupled systems: PhD Thesis. University of Surrey
    • Terry J. R. (2000). Synchronization of coupled systems: PhD Thesis. University of Surrey.
    • (2000)
    • Terry, J.R.1
  • 54
    • 0000631656 scopus 로고
    • Period-doublings to chaos in a simple neural network: An analytic proof
    • Wang, X. (1991). Period-doublings to chaos in a simple neural network: An analytic proof. Complex Systems, 5, 425-441.
    • (1991) Complex Systems , vol.5 , pp. 425-441
    • Wang, X.1
  • 55
    • 0000720835 scopus 로고
    • Cooperative phenomena in a homogenous cortical tissue model
    • H. Haken (Ed.). Stuttgart: B. G. Teubner
    • Wilson, H. R. (1973). Cooperative phenomena in a homogenous cortical tissue model. In H. Haken (Ed.), Synergetics - Cooperative Phenomena in Multi-Compartment Systems. Stuttgart: B. G. Teubner.
    • (1973) Synergetics - Cooperative Phenomena in Multi-Compartment Systems
    • Wilson, H.R.1
  • 56
    • 0015868589 scopus 로고
    • A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
    • Wilson, H. R., & Cowen, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetic, 13, 55-80.
    • (1973) Kybernetic , vol.13 , pp. 55-80
    • Wilson, H.R.1    Cowen, J.D.2
  • 57
    • 0022376719 scopus 로고
    • State changes in the brain viewed as linear steady-states and nonlinear transitions between steady-states
    • Wright J. J., Kydd, R., & Lees G. (1985). State changes in the brain viewed as linear steady-states and nonlinear transitions between steady-states. Biological Cybernetics, 53, 11-17.
    • (1985) Biological Cybernetics , vol.53 , pp. 11-17
    • Wright, J.J.1    Kydd, R.2    Lees, G.3
  • 58
    • 0029831991 scopus 로고    scopus 로고
    • Dynamics of the brain at global and microscopic scales. Neural networks and the EEG
    • Wright, J. J., & Liley, D. T. (1996). Dynamics of the brain at global and microscopic scales. Neural networks and the EEG. Behavioural and Brain Sciences, 19, 285-320.
    • (1996) Behavioural and Brain Sciences , vol.19 , pp. 285-320
    • Wright, J.J.1    Liley, D.T.2
  • 59
    • 11044238165 scopus 로고    scopus 로고
    • Modelling the whole brain in action
    • E. Gordon (Ed.). London: Harwood Academic Press
    • Wright, J. J. (2000). Modelling the whole brain in action. In E. Gordon (Ed.), Integrative Neuroscience. London: Harwood Academic Press.
    • (2000) Integrative Neuroscience
    • Wright, J.J.1
  • 60
    • 0001737375 scopus 로고    scopus 로고
    • Synchronization of chaotic systems and on-off intermittency
    • Yang, H., & Ding, E. (1996). Synchronization of chaotic systems and on-off intermittency. Physical Review E, 54, 1361-1365.
    • (1996) Physical Review E , vol.54 , pp. 1361-1365
    • Yang, H.1    Ding, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.