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Volumn 2, Issue , 2002, Pages 93-146

Chapter 3 Geometric singular perturbation analysis of neuronal dynamics

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EID: 67649321652     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80024-8     Document Type: Chapter
Times cited : (88)

References (98)
  • 1
    • 0021982751 scopus 로고
    • The generation and modulation of endogenous rhythmicity in the aplysia bursting pacemaker neurone R15
    • Adams W.B., and Benson J.A. The generation and modulation of endogenous rhythmicity in the aplysia bursting pacemaker neurone R15. Prog. Biophys. Mol. Biol. 46 (1985) 1-49
    • (1985) Prog. Biophys. Mol. Biol. , vol.46 , pp. 1-49
    • Adams, W.B.1    Benson, J.A.2
  • 2
    • 0003130734 scopus 로고
    • The slow passage through a Hopf bifurcation: delay, memory effects, and resonances
    • Baer S.M., Erneux T., and Rinzel J. The slow passage through a Hopf bifurcation: delay, memory effects, and resonances. SIAM J. Appl. Math. 49 (1989) 55-71
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 55-71
    • Baer, S.M.1    Erneux, T.2    Rinzel, J.3
  • 3
    • 0030220838 scopus 로고    scopus 로고
    • What stops synchronized thalamocortical oscillations?
    • Bal T., and McCormick D.A. What stops synchronized thalamocortical oscillations?. Neuron 17 (1996) 297-308
    • (1996) Neuron , vol.17 , pp. 297-308
    • Bal, T.1    McCormick, D.A.2
  • 4
    • 0029303855 scopus 로고
    • Topological and phenomenological classification of bursting oscillations
    • Bertram R., Butte M.J., Kiemel T., and Sherman A. Topological and phenomenological classification of bursting oscillations. Bull. Math. Biol. 57 (1995) 413-439
    • (1995) Bull. Math. Biol. , vol.57 , pp. 413-439
    • Bertram, R.1    Butte, M.J.2    Kiemel, T.3    Sherman, A.4
  • 5
    • 0346053690 scopus 로고    scopus 로고
    • Almost-synchronous solutions for networks of neurons coupled by excitation
    • Bose A., Kopell N., and Terman D. Almost-synchronous solutions for networks of neurons coupled by excitation. Phys. D 140 (2000) 69-94
    • (2000) Phys. D , vol.140 , pp. 69-94
    • Bose, A.1    Kopell, N.2    Terman, D.3
  • 6
    • 0030056795 scopus 로고    scopus 로고
    • Inhibition synchronizes sparsely connected cortical neurons within and between columns of realistic network models
    • Bush P., and Sejnowski T. Inhibition synchronizes sparsely connected cortical neurons within and between columns of realistic network models. J. Comput. Neurosci. (1996) 91-110
    • (1996) J. Comput. Neurosci. , pp. 91-110
    • Bush, P.1    Sejnowski, T.2
  • 7
    • 0344848562 scopus 로고    scopus 로고
    • Models of respiratory rhythm generation in the pre-Botzinger complex: I. Bursting pacemaker model
    • Butera R.J., Rinzel J., and Smith J.C. Models of respiratory rhythm generation in the pre-Botzinger complex: I. Bursting pacemaker model. J. Neurophysiology 82 (1999) 382-397
    • (1999) J. Neurophysiology , vol.82 , pp. 382-397
    • Butera, R.J.1    Rinzel, J.2    Smith, J.C.3
  • 8
    • 0344416993 scopus 로고    scopus 로고
    • Models of respiratory rhythm generation in the pre-Botzinger complex: II. Populations of coupled pacemaker neurons
    • Butera R.J., Rinzel J., and Smith J.C. Models of respiratory rhythm generation in the pre-Botzinger complex: II. Populations of coupled pacemaker neurons. J. Neurophysiology 82 (1999) 398-415
    • (1999) J. Neurophysiology , vol.82 , pp. 398-415
    • Butera, R.J.1    Rinzel, J.2    Smith, J.C.3
  • 9
    • 0004016751 scopus 로고
    • Buzsáki G., Llinás R., Singer W., Berthoz A., and Christen Y. (Eds), Springer, Berlin
    • In: Buzsáki G., Llinás R., Singer W., Berthoz A., and Christen Y. (Eds). Temporal Coding in the Brain (1994), Springer, Berlin
    • (1994) Temporal Coding in the Brain
  • 10
    • 0020957719 scopus 로고
    • Minimal model for membrane oscillations in the pancreatic β-cell
    • Chay T.R., and Keizer J. Minimal model for membrane oscillations in the pancreatic β-cell. Biophys. J. 42 (1983) 181-190
    • (1983) Biophys. J. , vol.42 , pp. 181-190
    • Chay, T.R.1    Keizer, J.2
  • 11
    • 0022037388 scopus 로고
    • Bursting beating and chaos in an excitable membrane model
    • Chay T.R., and Rinzel J. Bursting beating and chaos in an excitable membrane model. Biophys. J. 47 (1985) 357-366
    • (1985) Biophys. J. , vol.47 , pp. 357-366
    • Chay, T.R.1    Rinzel, J.2
  • 12
    • 0001380222 scopus 로고    scopus 로고
    • Phaselocking in weakly heterogeneous neuronal networks
    • Chow C.C. Phaselocking in weakly heterogeneous neuronal networks. Phys. D 118 (1998) 343-370
    • (1998) Phys. D , vol.118 , pp. 343-370
    • Chow, C.C.1
  • 13
    • 0003448521 scopus 로고
    • Cohen A.H., Rossignol S., and Grillner S. (Eds), Wiley, New York
    • In: Cohen A.H., Rossignol S., and Grillner S. (Eds). Neural Control of Rhythmic Movements in Vertebrates (1988), Wiley, New York
    • (1988) Neural Control of Rhythmic Movements in Vertebrates
  • 14
    • 0040066961 scopus 로고    scopus 로고
    • Corical and thalamic participation in the generation of seizures after blockage of inhibition
    • Contreras D., Destexhe A., and Steriade M. Corical and thalamic participation in the generation of seizures after blockage of inhibition. Soc. Neurosci. Abstracts 22 (1996) 2099
    • (1996) Soc. Neurosci. Abstracts , vol.22 , pp. 2099
    • Contreras, D.1    Destexhe, A.2    Steriade, M.3
  • 15
    • 0025738293 scopus 로고
    • Pancreatic β-cells are bursting, but how?
    • Cook L.D., Satin L.S., and Hopkins W.F. Pancreatic β-cells are bursting, but how?. Trends Neurosci. 14 (1991) 411-414
    • (1991) Trends Neurosci. , vol.14 , pp. 411-414
    • Cook, L.D.1    Satin, L.S.2    Hopkins, W.F.3
  • 16
    • 0032049163 scopus 로고    scopus 로고
    • Analysis of a class of models of bursting electrical activity in pancreatic β-cells
    • deVries G., and Miura R.M. Analysis of a class of models of bursting electrical activity in pancreatic β-cells. SIAM J. Appl. Math. 58 (1998) 607-635
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 607-635
    • deVries, G.1    Miura, R.M.2
  • 17
    • 0032213270 scopus 로고    scopus 로고
    • B receptors
    • B receptors. J. Neurosci. 18 (1998) 9099-9111
    • (1998) J. Neurosci. , vol.18 , pp. 9099-9111
    • Destexhe, A.1
  • 18
    • 0027443835 scopus 로고
    • Ionic mechanisms for intrinsic slow oscillations in thalamic relay and reticularis neurons
    • Destexhe A., Babloyantz A., and Sejnowski T.J. Ionic mechanisms for intrinsic slow oscillations in thalamic relay and reticularis neurons. Biophys. J. 65 (1993) 1538-1552
    • (1993) Biophys. J. , vol.65 , pp. 1538-1552
    • Destexhe, A.1    Babloyantz, A.2    Sejnowski, T.J.3
  • 19
    • 0029785642 scopus 로고    scopus 로고
    • Ionic mechanisms underlying synchronized oscilla-tions and propagating waves in a model of ferret thalamic slices
    • Destexhe A., Bal T., McCormick D., and Sejnowski T. Ionic mechanisms underlying synchronized oscilla-tions and propagating waves in a model of ferret thalamic slices. J. Neurophysi. 76 (1996) 2049-2070
    • (1996) J. Neurophysi. , vol.76 , pp. 2049-2070
    • Destexhe, A.1    Bal, T.2    McCormick, D.3    Sejnowski, T.4
  • 20
    • 0038882499 scopus 로고    scopus 로고
    • Cortical projections to the thalamic reticular nucleus may control the spatiotemporal coherence of spindle and epileptic oscillations
    • Destexhe A., Contreras D., Sejnowski T.J., and Steriade M. Cortical projections to the thalamic reticular nucleus may control the spatiotemporal coherence of spindle and epileptic oscillations. Soc. Neurosci. Abstracts 22 (1996) 2099
    • (1996) Soc. Neurosci. Abstracts , vol.22 , pp. 2099
    • Destexhe, A.1    Contreras, D.2    Sejnowski, T.J.3    Steriade, M.4
  • 21
    • 0027132059 scopus 로고
    • A model for 8-10 Hz spindling in interconnected thala-mic relay and reticularis neurons
    • Destexhe A., McCormick D.A., and Sejnowski T.J. A model for 8-10 Hz spindling in interconnected thala-mic relay and reticularis neurons. Biophys. J. 65 (1993) 2474-2478
    • (1993) Biophys. J. , vol.65 , pp. 2474-2478
    • Destexhe, A.1    McCormick, D.A.2    Sejnowski, T.J.3
  • 22
    • 0002279331 scopus 로고    scopus 로고
    • Synchronized oscillations in thalamic networks: insights from modeling studies
    • Steriade M., Jones E., and McCormick D. (Eds), Elsevier, Amsterdam
    • Destexhe A., and Sejnowski T. Synchronized oscillations in thalamic networks: insights from modeling studies. In: Steriade M., Jones E., and McCormick D. (Eds). Thalamus Vol. II (1997), Elsevier, Amsterdam 331-372
    • (1997) Thalamus , vol.II , pp. 331-372
    • Destexhe, A.1    Sejnowski, T.2
  • 23
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory
    • Fenichel N. Geometric singular perturbation theory. J. Differential Equations 31 (1979) 53-91
    • (1979) J. Differential Equations , vol.31 , pp. 53-91
    • Fenichel, N.1
  • 24
    • 0028589640 scopus 로고
    • Reciprocal inhibition, a mechanism underlying oscillatory animal movements
    • Friesen W. Reciprocal inhibition, a mechanism underlying oscillatory animal movements. Neurosci. Be-havior 18 (1994) 547-553
    • (1994) Neurosci. Be-havior , vol.18 , pp. 547-553
    • Friesen, W.1
  • 26
    • 0001297707 scopus 로고
    • Dynamics of globally coupled inhibitory neurons with heterogeneity
    • Golomb D., and Rinzel J. Dynamics of globally coupled inhibitory neurons with heterogeneity. Phys. Rev. E 48 (1993) 4810-4814
    • (1993) Phys. Rev. E , vol.48 , pp. 4810-4814
    • Golomb, D.1    Rinzel, J.2
  • 27
    • 0000399729 scopus 로고
    • Clustering in globally coupled inhibitory neurons
    • Golomb D., and Rinzel J. Clustering in globally coupled inhibitory neurons. Phys. D 72 (1994) 259-282
    • (1994) Phys. D , vol.72 , pp. 259-282
    • Golomb, D.1    Rinzel, J.2
  • 28
    • 0028048720 scopus 로고
    • Synchronization properties of spindle oscillations in a thalamic reticular nucleus model
    • Golomb D., Wang X.-J., and Rinzel J. Synchronization properties of spindle oscillations in a thalamic reticular nucleus model. J. Neurophysiol. 72 (1994) 1109-1126
    • (1994) J. Neurophysiol. , vol.72 , pp. 1109-1126
    • Golomb, D.1    Wang, X.-J.2    Rinzel, J.3
  • 29
    • 0029976329 scopus 로고    scopus 로고
    • Propagation of spindle waves in a thalamic slice model
    • Golomb D., Wang X.-J., and Rinzel J. Propagation of spindle waves in a thalamic slice model. J. Neuro-physiol. 75 (1996) 750-769
    • (1996) J. Neuro-physiol. , vol.75 , pp. 750-769
    • Golomb, D.1    Wang, X.-J.2    Rinzel, J.3
  • 30
    • 0028457501 scopus 로고
    • Synchronous oscillations in neuronal systems: Mechanisms and functions
    • Gray C.M. Synchronous oscillations in neuronal systems: Mechanisms and functions. J. Comput. Neurosci. 1 (1994) 11-38
    • (1994) J. Comput. Neurosci. , vol.1 , pp. 11-38
    • Gray, C.M.1
  • 31
    • 0029742202 scopus 로고    scopus 로고
    • Chattering cells: Superficial pyramidal neurons contributing to the gen-eration of synchronous oscillations in the visual cortex
    • Gray C.M., and McCormick D.A. Chattering cells: Superficial pyramidal neurons contributing to the gen-eration of synchronous oscillations in the visual cortex. Science 274 (1996) 109-113
    • (1996) Science , vol.274 , pp. 109-113
    • Gray, C.M.1    McCormick, D.A.2
  • 32
    • 0021768729 scopus 로고
    • A model of neuronal bursting using three coupled first order differential equations
    • Hindmarsh J.L., and Rose R.M. A model of neuronal bursting using three coupled first order differential equations. Proc. Roy Soc. London Ser. B 221 (1984) 87-102
    • (1984) Proc. Roy Soc. London Ser. B , vol.221 , pp. 87-102
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 33
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in a nerve
    • Hodgkin A.L., and Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in a nerve. J. Physiol. 117 (1952) 165-181
    • (1952) J. Physiol. , vol.117 , pp. 165-181
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 35
    • 0028174189 scopus 로고
    • b-mediated inhibition in thalamic relay neurons through effects in nucleus reticularis
    • b-mediated inhibition in thalamic relay neurons through effects in nucleus reticularis. J. Neurophysiol. 71 (1994) 2576-2581
    • (1994) J. Neurophysiol. , vol.71 , pp. 2576-2581
    • Huguenard, J.1    Prince, D.2
  • 36
    • 0033593590 scopus 로고    scopus 로고
    • Reciprocal inhibitory connections and network synchrony in the mammalian thalamus
    • Huntsman M., Porcello D., Homanics G., DeLorey T., and Huguenard J. Reciprocal inhibitory connections and network synchrony in the mammalian thalamus. Science 283 (1999) 541-543
    • (1999) Science , vol.283 , pp. 541-543
    • Huntsman, M.1    Porcello, D.2    Homanics, G.3    DeLorey, T.4    Huguenard, J.5
  • 38
    • 0003963813 scopus 로고
    • Jacklet J.W. (Ed), Marcel Dekker, New York
    • In: Jacklet J.W. (Ed). Neuronal and Cellular Oscillators (1989), Marcel Dekker, New York
    • (1989) Neuronal and Cellular Oscillators
  • 41
    • 0029076314 scopus 로고
    • Spindle waves are propagating synchronized oscillations in the ferret LGNd in vitro
    • Kim U., Bal T., and McCormick D.A. Spindle waves are propagating synchronized oscillations in the ferret LGNd in vitro. J. Neurophysiol. 74 (1995) 1301-1323
    • (1995) J. Neurophysiol. , vol.74 , pp. 1301-1323
    • Kim, U.1    Bal, T.2    McCormick, D.A.3
  • 42
    • 38249043593 scopus 로고
    • Subcellular oscillations and bursting
    • Kopell N., and Ermentrout G.B. Subcellular oscillations and bursting. Math. Biosci. 78 (1986) 265-291
    • (1986) Math. Biosci. , vol.78 , pp. 265-291
    • Kopell, N.1    Ermentrout, G.B.2
  • 43
    • 67649372867 scopus 로고    scopus 로고
    • Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators
    • Fiedler B. (Ed), Elsevier, Amsterdam
    • Kopell N., and Ermentrout B. Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. In: Fiedler B. (Ed). Handbook of Dynamical Systems Vol. 2 (2002), Elsevier, Amsterdam 3-54
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 3-54
    • Kopell, N.1    Ermentrout, B.2
  • 44
    • 0027943271 scopus 로고
    • Rhythmogenesis amplitude modulation and multiplexing in a cortical archi-tecture
    • Kopell N., and LeMasson G. Rhythmogenesis amplitude modulation and multiplexing in a cortical archi-tecture. Proc. Nat. Acad. Sci. USA 91 (1994) 10586-10590
    • (1994) Proc. Nat. Acad. Sci. USA , vol.91 , pp. 10586-10590
    • Kopell, N.1    LeMasson, G.2
  • 45
    • 0029206717 scopus 로고
    • Anti-phase solutions in relaxation oscillators coupled through excitatory synapses
    • Kopell N., and Somers D. Anti-phase solutions in relaxation oscillators coupled through excitatory synapses. J. Math. Biol. 33 (1995) 261-280
    • (1995) J. Math. Biol. , vol.33 , pp. 261-280
    • Kopell, N.1    Somers, D.2
  • 46
    • 21944438553 scopus 로고    scopus 로고
    • Uniqueness and stability of periodic bursting solutions
    • Lee E., and Terman D. Uniqueness and stability of periodic bursting solutions. J. Differential Equations 158 (1999) 48-78
    • (1999) J. Differential Equations , vol.158 , pp. 48-78
    • Lee, E.1    Terman, D.2
  • 47
    • 0024239764 scopus 로고
    • The intrinsic electrophysiological properties of mammalian neurons: Insights into central ner-vous system function
    • Llinás R.R. The intrinsic electrophysiological properties of mammalian neurons: Insights into central ner-vous system function. Science 242 (1988) 1654-1664
    • (1988) Science , vol.242 , pp. 1654-1664
    • Llinás, R.R.1
  • 48
    • 0025972273 scopus 로고
    • In vitro neurons in mammalian cortical layer 4 exhibit intrinsic oscil-latory activity in the 10-to 50-Hz frequency range
    • Llinás R.R., Grace T., and Yarom Y. In vitro neurons in mammalian cortical layer 4 exhibit intrinsic oscil-latory activity in the 10-to 50-Hz frequency range. Proc. Nat. Acad. Sci. USA 88 (1991) 897-901
    • (1991) Proc. Nat. Acad. Sci. USA , vol.88 , pp. 897-901
    • Llinás, R.R.1    Grace, T.2    Yarom, Y.3
  • 49
    • 0033144266 scopus 로고    scopus 로고
    • Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map
    • LoFaro T., and Kopell N. Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map. J. Math. Biol. 38 (1999) 479-533
    • (1999) J. Math. Biol. , vol.38 , pp. 479-533
    • LoFaro, T.1    Kopell, N.2
  • 51
    • 0019405994 scopus 로고
    • Voltage oscillations in the barnicle giant muscle fiber
    • Morris C., and Lecar H. Voltage oscillations in the barnicle giant muscle fiber. Biophys. J. 35 (1981) 193-213
    • (1981) Biophys. J. , vol.35 , pp. 193-213
    • Morris, C.1    Lecar, H.2
  • 52
    • 0031837976 scopus 로고    scopus 로고
    • Evidence for a novel bursting mechanism in rodent trigeminal neurons
    • Negro C.A.D., Hsiao C.-F., Chandler S.H., and Garfinkel A. Evidence for a novel bursting mechanism in rodent trigeminal neurons. Biophys. J. 75 (1998) 174-182
    • (1998) Biophys. J. , vol.75 , pp. 174-182
    • Negro, C.A.D.1    Hsiao, C.-F.2    Chandler, S.H.3    Garfinkel, A.4
  • 53
    • 0001445993 scopus 로고
    • Asymptotic investigation of the loss of stability by an equilibrium as a pair of eigenvalues slowly cross the imaginary axis
    • Neishtadt A. Asymptotic investigation of the loss of stability by an equilibrium as a pair of eigenvalues slowly cross the imaginary axis. Uspekhi Mat. Nauk 40 (1985) 190-191
    • (1985) Uspekhi Mat. Nauk , vol.40 , pp. 190-191
    • Neishtadt, A.1
  • 54
    • 0028444759 scopus 로고
    • Fast subsystem bifurcations in a slowly varying Lienard system exhibiting bursting
    • Pernarowski M. Fast subsystem bifurcations in a slowly varying Lienard system exhibiting bursting. SIAM J. Appl. Math. 54 (1994) 814-832
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 814-832
    • Pernarowski, M.1
  • 55
    • 0028457466 scopus 로고
    • Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons
    • Pinsky P., and Rinzel J. Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J. Comput. Neurosci. 1 (1994) 39-60
    • (1994) J. Comput. Neurosci. , vol.1 , pp. 39-60
    • Pinsky, P.1    Rinzel, J.2
  • 56
    • 0019351545 scopus 로고
    • Bifurcation and resonance in a model for bursting nerve cells
    • Plant R.E. Bifurcation and resonance in a model for bursting nerve cells. J. Math. Biol. 11 (1981) 15-32
    • (1981) J. Math. Biol. , vol.11 , pp. 15-32
    • Plant, R.E.1
  • 57
    • 0000117122 scopus 로고
    • Bursting oscillations in an excitable membrane model
    • Sleeman B.D., and Jarvis R.J. (Eds), Springer, New York
    • Rinzel J. Bursting oscillations in an excitable membrane model. In: Sleeman B.D., and Jarvis R.J. (Eds). Ordinary and Partial Differential Equations (1985), Springer, New York
    • (1985) Ordinary and Partial Differential Equations
    • Rinzel, J.1
  • 58
    • 0002356724 scopus 로고
    • A formal classification of bursting mechanisms in excitable systems
    • Gleason A.M. (Ed), Amer. Math. Soc, Providence, RI
    • Rinzel J. A formal classification of bursting mechanisms in excitable systems. In: Gleason A.M. (Ed). Proceedings of the International Congress of Mathematicians (1987), Amer. Math. Soc, Providence, RI 1578-1594
    • (1987) Proceedings of the International Congress of Mathematicians , pp. 1578-1594
    • Rinzel, J.1
  • 59
    • 0002453062 scopus 로고    scopus 로고
    • Analysis of neural excitability and oscillations
    • Koch C., and Segev I. (Eds), MIT Press, Cambridge, MA
    • Rinzel J., and Ermentrout G.B. Analysis of neural excitability and oscillations. In: Koch C., and Segev I. (Eds). Methods in Neuronal Modeling: From Ions to Networks. 2nd edn. (1998), MIT Press, Cambridge, MA 251-291
    • (1998) Methods in Neuronal Modeling: From Ions to Networks. 2nd edn. , pp. 251-291
    • Rinzel, J.1    Ermentrout, G.B.2
  • 60
    • 0023461032 scopus 로고
    • Dissection of a model for neuronal parabolic bursting
    • Rinzel J., and Lee YS. Dissection of a model for neuronal parabolic bursting. J. Math. Biol. 25 (1987) 653-657
    • (1987) J. Math. Biol. , vol.25 , pp. 653-657
    • Rinzel, J.1    Lee, YS.2
  • 61
    • 0032570706 scopus 로고    scopus 로고
    • Propagating activity patterns in large-scale inhibitory neuronal networks
    • Rinzel J., Terman D., Wang X.-J., and Ermentrout B. Propagating activity patterns in large-scale inhibitory neuronal networks. Science 279 (1998) 1351-1355
    • (1998) Science , vol.279 , pp. 1351-1355
    • Rinzel, J.1    Terman, D.2    Wang, X.-J.3    Ermentrout, B.4
  • 62
    • 0034576375 scopus 로고    scopus 로고
    • Analysis of clustered firing patterns in synaptically coupled networks of oscillators
    • Rubin J., and Terman D. Analysis of clustered firing patterns in synaptically coupled networks of oscillators. J. Math. Biol. 41 (2000) 513-545
    • (2000) J. Math. Biol. , vol.41 , pp. 513-545
    • Rubin, J.1    Terman, D.2
  • 63
    • 0034150797 scopus 로고    scopus 로고
    • Geometric analysis of population rhythms in synaptically coupled neuronal networks
    • Rubin J., and Terman D. Geometric analysis of population rhythms in synaptically coupled neuronal networks. Neural Comput. 12 (2000) 597-645
    • (2000) Neural Comput. , vol.12 , pp. 597-645
    • Rubin, J.1    Terman, D.2
  • 64
    • 67649328087 scopus 로고    scopus 로고
    • Geometric analysis of population rhythms in synaptically coupled neuronal net-works
    • Rubin J., and Terman D. Geometric analysis of population rhythms in synaptically coupled neuronal net-works. IMA Preprint Series # 1586 (1998)
    • (1998) IMA Preprint Series # , vol.1586
    • Rubin, J.1    Terman, D.2
  • 65
    • 17144449149 scopus 로고    scopus 로고
    • Geometric analysis of neuronal firing patterns in network models with fast in-hibitory synapses
    • Rubin J., and Terman D. Geometric analysis of neuronal firing patterns in network models with fast in-hibitory synapses. Neurocomputing 26-27 (1999) 491-498
    • (1999) Neurocomputing , vol.26-27 , pp. 491-498
    • Rubin, J.1    Terman, D.2
  • 66
    • 0028500362 scopus 로고
    • Anti-phase asymmetric and aperiodic oscillations in excitable cells-I. coupled bursters
    • Sherman A. Anti-phase asymmetric and aperiodic oscillations in excitable cells-I. coupled bursters. Bull. Math. Biol. 56 (1994) 811-835
    • (1994) Bull. Math. Biol. , vol.56 , pp. 811-835
    • Sherman, A.1
  • 67
    • 0029784059 scopus 로고    scopus 로고
    • Contributions of modeling to understanding stimulus-secretion coupling in pancreatic β-cells
    • Sherman A. Contributions of modeling to understanding stimulus-secretion coupling in pancreatic β-cells. Amer. J. Physiology 271 (1996) 547-559
    • (1996) Amer. J. Physiology , vol.271 , pp. 547-559
    • Sherman, A.1
  • 68
    • 0028457504 scopus 로고
    • Mechanisms for oscillation and frequency control in networks of mutually inhibitory relaxation oscillators
    • Skinner F., Kopell N., and Marder E. Mechanisms for oscillation and frequency control in networks of mutually inhibitory relaxation oscillators. J. Comput. Neurosci. 1 (1994) 69-87
    • (1994) J. Comput. Neurosci. , vol.1 , pp. 69-87
    • Skinner, F.1    Kopell, N.2    Marder, E.3
  • 69
    • 0027161335 scopus 로고
    • Why pancreatic islets burst but single β-cells do not: The heterogene-ity hypothesis
    • Smolen P., Rinzel J., and Sherman A. Why pancreatic islets burst but single β-cells do not: The heterogene-ity hypothesis. Biophys. J. 64 (1993) 1668-1680
    • (1993) Biophys. J. , vol.64 , pp. 1668-1680
    • Smolen, P.1    Rinzel, J.2    Sherman, A.3
  • 70
    • 0027608561 scopus 로고
    • Properties of a bursting model with two slow inhibitory variables
    • Smolen P., Terman D., and Rinzel J. Properties of a bursting model with two slow inhibitory variables. SIAM J. Appl. Math. 53 (1993) 861-892
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 861-892
    • Smolen, P.1    Terman, D.2    Rinzel, J.3
  • 71
    • 0027344291 scopus 로고
    • Rapid synchronization through fast threshold modulation
    • Somers D., and Kopell N. Rapid synchronization through fast threshold modulation. Biol. Cybern. 68 (1993) 393-407
    • (1993) Biol. Cybern. , vol.68 , pp. 393-407
    • Somers, D.1    Kopell, N.2
  • 72
    • 0000394358 scopus 로고
    • Waves and synchrony in networks of oscillators of relaxation and non-relaxation type
    • Somers D., and Kopell N. Waves and synchrony in networks of oscillators of relaxation and non-relaxation type. Phys. D 89 (1995) 169-183
    • (1995) Phys. D , vol.89 , pp. 169-183
    • Somers, D.1    Kopell, N.2
  • 74
    • 0039475146 scopus 로고
    • Coherent activities in corticothalamic networks during resting sleep and their development into paroxysmal events
    • Buzsáki G., Llinás R., Singer W., Berthoz A., and Christen Y. (Eds), Springer, Berlin
    • Steriade M. Coherent activities in corticothalamic networks during resting sleep and their development into paroxysmal events. In: Buzsáki G., Llinás R., Singer W., Berthoz A., and Christen Y. (Eds). Temporal Coding in the Brain (1994), Springer, Berlin
    • (1994) Temporal Coding in the Brain
    • Steriade, M.1
  • 75
    • 43949154216 scopus 로고
    • Synchronized sleep oscillations and their paroxysmal develop-ments
    • Steriade M., Contreras D., and Amzica F. Synchronized sleep oscillations and their paroxysmal develop-ments. Trends Neurosci. 17 (1994) 199-208
    • (1994) Trends Neurosci. , vol.17 , pp. 199-208
    • Steriade, M.1    Contreras, D.2    Amzica, F.3
  • 76
    • 0000849631 scopus 로고    scopus 로고
    • The thalamocortical dialogue during wake, sleep, and paroxysmal oscillations
    • Steriade M., Jones E., and McCormick D. (Eds), Elsevier, Amsterdam
    • Steriade M., Contreras D., and Amzica F. The thalamocortical dialogue during wake, sleep, and paroxysmal oscillations. In: Steriade M., Jones E., and McCormick D. (Eds). Thalamus Vol. II (1997), Elsevier, Amsterdam 213-294
    • (1997) Thalamus , vol.II , pp. 213-294
    • Steriade, M.1    Contreras, D.2    Amzica, F.3
  • 77
    • 0023145045 scopus 로고
    • Abolition of spindle oscillations in thalamic neurons disconnected from nucleus reticularis thalami
    • Steriade M., Domich L., Oakson G., and Deschênes M. Abolition of spindle oscillations in thalamic neurons disconnected from nucleus reticularis thalami. J. Neurophysiol. 57 (1987) 260-273
    • (1987) J. Neurophysiol. , vol.57 , pp. 260-273
    • Steriade, M.1    Domich, L.2    Oakson, G.3    Deschênes, M.4
  • 78
    • 0004226462 scopus 로고    scopus 로고
    • Steriade M., Jones E., and McCormick D. (Eds), Elsevier, Amsterdam
    • In: Steriade M., Jones E., and McCormick D. (Eds). Thalamus Vol. II (1997), Elsevier, Amsterdam
    • (1997) Thalamus , vol.II
  • 80
    • 0027445242 scopus 로고
    • Thalamocortical oscillations in the sleep and aroused brain
    • Steriade M., McCormick D.A., and Sejnowski T.J. Thalamocortical oscillations in the sleep and aroused brain. Science 262 (1993) 679-685
    • (1993) Science , vol.262 , pp. 679-685
    • Steriade, M.1    McCormick, D.A.2    Sejnowski, T.J.3
  • 81
    • 0032858916 scopus 로고    scopus 로고
    • Comparison of two models for pattern generation based on synaptic depression
    • Tabak J., Senn W., O'Donovan M.J., and Rinzel J. Comparison of two models for pattern generation based on synaptic depression. Neurocomputing 26-27 (1999) 551-556
    • (1999) Neurocomputing , vol.26-27 , pp. 551-556
    • Tabak, J.1    Senn, W.2    O'Donovan, M.J.3    Rinzel, J.4
  • 82
    • 0026239399 scopus 로고
    • Chaotic spikes arising from a model for bursting in excitable membranes
    • Terman D. Chaotic spikes arising from a model for bursting in excitable membranes. SIAM J. Appl. Math. 51 (1991) 1418-1450
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 1418-1450
    • Terman, D.1
  • 83
    • 34249839599 scopus 로고
    • The transition from bursting to continuous spiking in an excitable membrane model
    • Terman D. The transition from bursting to continuous spiking in an excitable membrane model. J. Nonlinear Sci. 2 (1992) 133-182
    • (1992) J. Nonlinear Sci. , vol.2 , pp. 133-182
    • Terman, D.1
  • 84
    • 0030447562 scopus 로고    scopus 로고
    • Functional reorganization in thalamocortical networks: Transition between spindling and delta sleep rhythms
    • Terman D., Bose A., and Kopell N. Functional reorganization in thalamocortical networks: Transition between spindling and delta sleep rhythms. Proc. Nat. Acad. Sci. USA 93 (1996) 15417-15422
    • (1996) Proc. Nat. Acad. Sci. USA , vol.93 , pp. 15417-15422
    • Terman, D.1    Bose, A.2    Kopell, N.3
  • 85
    • 0000821114 scopus 로고    scopus 로고
    • Dynamics of two mutually coupled inhibitory neurons
    • Terman D., Kopell N., and Bose A. Dynamics of two mutually coupled inhibitory neurons. Phys. D 117 (1998) 241-275
    • (1998) Phys. D , vol.117 , pp. 241-275
    • Terman, D.1    Kopell, N.2    Bose, A.3
  • 86
    • 0031077119 scopus 로고    scopus 로고
    • Partial synchronization in a network of neural oscillators
    • Terman D., and Lee E. Partial synchronization in a network of neural oscillators. SIAM J. Appl. Math. 57 (1997) 252-293
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 252-293
    • Terman, D.1    Lee, E.2
  • 87
    • 58149210859 scopus 로고
    • Global competition and local cooperation in a network of neural oscillators
    • Terman D., and Wang D.L. Global competition and local cooperation in a network of neural oscillators. Phys. D 81 (1995) 148-176
    • (1995) Phys. D , vol.81 , pp. 148-176
    • Terman, D.1    Wang, D.L.2
  • 88
    • 0035178331 scopus 로고    scopus 로고
    • Geometric singular perturbation analysis of wave propaga-tion in thalamic networks
    • Terman D.H., Ermentrout G.B., and Yew A.C. Geometric singular perturbation analysis of wave propaga-tion in thalamic networks. SIAM J. Appl. Math. 61 (2001) 1578-1604
    • (2001) SIAM J. Appl. Math. , vol.61 , pp. 1578-1604
    • Terman, D.H.1    Ermentrout, G.B.2    Yew, A.C.3
  • 90
    • 0028679412 scopus 로고
    • When inhibition, not excitation, synchronizes neural firing
    • Vreeswijk C.v., Abbott L., and Ermentrout G.B. When inhibition, not excitation, synchronizes neural firing. J. Comput. Neurosci. 1 (1994) 313-321
    • (1994) J. Comput. Neurosci. , vol.1 , pp. 313-321
    • Vreeswijk, C.v.1    Abbott, L.2    Ermentrout, G.B.3
  • 91
    • 0029206489 scopus 로고
    • Locally excitatory globally inhibitory oscillator networks
    • Wang D.L., and Terman D. Locally excitatory globally inhibitory oscillator networks. IEEE Trans. Neural Nets 6 (1995) 283-286
    • (1995) IEEE Trans. Neural Nets , vol.6 , pp. 283-286
    • Wang, D.L.1    Terman, D.2
  • 92
    • 0027717216 scopus 로고
    • Ionic basis for intrinsic-40 Hz neuronal oscillations
    • Wang X.-J. Ionic basis for intrinsic-40 Hz neuronal oscillations. Neuroreport 5 (1993) 221-224
    • (1993) Neuroreport , vol.5 , pp. 221-224
    • Wang, X.-J.1
  • 93
    • 0029075505 scopus 로고
    • Emergent spindle oscillations and intermittent burst firing in a thala-mic model: specific neuronal mechanisms
    • Wang X.-J., Golomb D., and Rinzel J. Emergent spindle oscillations and intermittent burst firing in a thala-mic model: specific neuronal mechanisms. Proc. Nat. Acad. Sci. USA 92 (1995) 5577-5581
    • (1995) Proc. Nat. Acad. Sci. USA , vol.92 , pp. 5577-5581
    • Wang, X.-J.1    Golomb, D.2    Rinzel, J.3
  • 94
    • 0003082358 scopus 로고
    • Alternating and synchronous rhythms in reciprocally inhibitory model neurons
    • Wang X.-J., and Rinzel J. Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Comput. 4 (1992) 84-97
    • (1992) Neural Comput. , vol.4 , pp. 84-97
    • Wang, X.-J.1    Rinzel, J.2
  • 95
    • 0027193370 scopus 로고
    • Spindle rhythmicity in the reticularis thalamic nucleus: synchronization among mutually inhibitory neurons
    • Wang X.-J., and Rinzel J. Spindle rhythmicity in the reticularis thalamic nucleus: synchronization among mutually inhibitory neurons. Neurosci. 53 (1993) 899-904
    • (1993) Neurosci. , vol.53 , pp. 899-904
    • Wang, X.-J.1    Rinzel, J.2
  • 96
    • 0001736010 scopus 로고
    • Oscillatory and bursting properties of neurons
    • Arbib M.A. (Ed), MIT Press, Cambridge, MA
    • Wang X.-J., and Rinzel J. Oscillatory and bursting properties of neurons. In: Arbib M.A. (Ed). The Handbook of Brain Theory and Neural Networks (1995), MIT Press, Cambridge, MA 686-691
    • (1995) The Handbook of Brain Theory and Neural Networks , pp. 686-691
    • Wang, X.-J.1    Rinzel, J.2
  • 97
    • 0031881939 scopus 로고    scopus 로고
    • Synchronization and oscillatory dynamics in heteroge-neous, mutually inhibited neurons
    • White J., Chow C.C., Ritt J., Soto C., and Kopell N. Synchronization and oscillatory dynamics in heteroge-neous, mutually inhibited neurons. J. Comput. Neurosci. 5 (1998) 5-16
    • (1998) J. Comput. Neurosci. , vol.5 , pp. 5-16
    • White, J.1    Chow, C.C.2    Ritt, J.3    Soto, C.4    Kopell, N.5
  • 98
    • 0028985211 scopus 로고
    • Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation
    • Whittington M.A., Traub R.D., and Jeffreys J.G.R. Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation. Nature 373 (1995) 612-615
    • (1995) Nature , vol.373 , pp. 612-615
    • Whittington, M.A.1    Traub, R.D.2    Jeffreys, J.G.R.3


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