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Volumn 12, Issue 3, 2013, Pages 1649-1684

Effects of heterogeneous periodic forcing on inhibitory networks

Author keywords

Inhibitory coupling; Invariant manifolds; Periodic forcing; Timing map

Indexed keywords

INHIBITORY COUPLING; INVARIANT MANIFOLDS; LARGE NETWORKS; MUTUAL INHIBITION; PERIODIC FORCING; PHASE RESPONSE CURVES; SINGLE OSCILLATORS;

EID: 84884958367     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/12089274X     Document Type: Article
Times cited : (9)

References (40)
  • 1
    • 65549117124 scopus 로고    scopus 로고
    • Phase resetting curves determine synchronization phase-locking and clustering in networks of neural oscillators
    • S. Achuthan and C. C. Canavier, Phase resetting curves determine synchronization, phase-locking, and clustering in networks of neural oscillators, J. Neurosci., 29 (2009), pp. 5218-5233.
    • (2009) J. Neurosci , vol.29 , pp. 5218-5233
    • Achuthan, S.1    Canavier, C.C.2
  • 2
    • 0032519003 scopus 로고    scopus 로고
    • The synaptic basis of GABAA slow
    • M. I. Banks, T. B. Li, and R. A. Pearce, The synaptic basis of GABAA, slow, J. Neurosci., 18 (1998), pp. 1305-1317.
    • (1998) J. Neurosci , vol.18 , pp. 1305-1317
    • Banks, M.I.1    Li, T.B.2    Pearce, R.A.3
  • 3
    • 0033860986 scopus 로고    scopus 로고
    • A network of electrically coupled interneurons drives synchronized inhibition in neocortex
    • M. Beierlein, J. R. Gibson, and B. W. Conners, A network of electrically coupled interneurons drives synchronized inhibition in neocortex, Nat. Neurosci., 3 (2000), pp. 904-910.
    • (2000) Nat. Neurosci , vol.3 , pp. 904-910
    • Beierlein, M.1    Gibson, J.R.2    Conners, B.W.3
  • 5
    • 77954144054 scopus 로고    scopus 로고
    • Pulse coupled oscillators and the phase resetting curve
    • C. C. Canavier and S. Achulthan, Pulse coupled oscillators and the phase resetting curve, Math. Biosci., 226 (2010), pp. 77-96.
    • (2010) Math. Biosci , vol.226 , pp. 77-96
    • Canavier, C.C.1    Achulthan, S.2
  • 6
    • 0031788753 scopus 로고    scopus 로고
    • Frequency control in synchronized networks of inhibitory neurons
    • C. C. Chow, J. A. White, J. Ritt, and N. Kopell, Frequency control in synchronized networks of inhibitory neurons, J. Comput. Neurosci., 5 (1998), pp. 407-420.
    • (1998) J. Comput. Neurosci , vol.5 , pp. 407-420
    • Chow, C.C.1    White, J.A.2    Ritt, J.3    Kopell, N.4
  • 7
    • 33748428043 scopus 로고    scopus 로고
    • A computational tool for the reduction of nonlinear ODE systems possessing multiple scales
    • R. Clewley, H. G. Rotstein, and N. Kopell, A computational tool for the reduction of nonlinear ODE systems possessing multiple scales, Multiscale Model. Simul., 4 (2005), pp. 732-759.
    • (2005) Multiscale Model. Simul , vol.4 , pp. 732-759
    • Clewley, R.1    Rotstein, H.G.2    Kopell, N.3
  • 8
    • 0032523522 scopus 로고    scopus 로고
    • Spike frequency adaptation affects the synchronization properties of networks of cortical oscillations
    • S. M. Crook, G. B. Ermentrout, and J. M. Bower, Spike frequency adaptation affects the synchronization properties of networks of cortical oscillations, Neural Comput., 10 (1998), pp. 837-854.
    • (1998) Neural Comput , vol.10 , pp. 837-854
    • Crook, S.M.1    Ermentrout, G.B.2    Bower, J.M.3
  • 11
    • 0035374850 scopus 로고    scopus 로고
    • The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators
    • B. Ermentrout, M. Pascal, and B. Gutkin, The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators, Neural Comput., 13 (2001), pp. 1285-1310.
    • (2001) Neural Comput , vol.13 , pp. 1285-1310
    • Ermentrout, B.1    Pascal, M.2    Gutkin, B.3
  • 12
    • 0032477877 scopus 로고    scopus 로고
    • Fine structure of neural spiking and synchronization in the presence of conduction delays
    • G. B. Ermentrout and N. Kopell, Fine structure of neural spiking and synchronization in the presence of conduction delays, Proc. Natl. Acad. Sci. USA, 95 (1998), pp. 1259-1264.
    • (1998) Proc. Natl. Acad. Sci. USA , vol.95 , pp. 1259-1264
    • Ermentrout, G.B.1    Kopell, N.2
  • 13
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations, 31 (1979), pp. 53-98.
    • (1979) J. Differential Equations , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 14
    • 33845884817 scopus 로고    scopus 로고
    • On the dynamics of electrically-coupled neurons with inhibitory synapses
    • J. Gao and P. Holmes, On the dynamics of electrically-coupled neurons with inhibitory synapses, J. Comput. Neurosci., 22 (2007), pp. 39-61.
    • (2007) J. Comput. Neurosci , vol.22 , pp. 39-61
    • Gao, J.1    Holmes, P.2
  • 18
    • 84884938840 scopus 로고    scopus 로고
    • Interactions of inhibitory cells
    • Ph.D. thesis, , Center for BioDynamics, Boston University, Boston, MA
    • B. Hedinsson, Interactions of Inhibitory Cells, Ph.D. thesis, Department of Mathematics and Statistics, Center for BioDynamics, Boston University, Boston, MA, 2011.
    • (2011) Department of Mathematics and Statistics
    • Hedinsson, B.1
  • 20
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • R. Johnson, ed., Springer, New York
    • C. K. Jones, Geometric singular perturbation theory, in Dynamical Systems, Lecture Notes in Math. 1609, R. Johnson, ed., Springer, New York, 1994, pp. 44-118.
    • (1994) Dynamical Systems, Lecture Notes in Math , vol.1609 , pp. 44-118
    • Jones, C.K.1
  • 21
    • 7444259575 scopus 로고    scopus 로고
    • Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks
    • N. Kopell and B. Ermentrout, Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 15482-15487.
    • (2004) Proc. Natl. Acad. Sci. USA , vol.101 , pp. 15482-15487
    • Kopell, N.1    Ermentrout, B.2
  • 22
    • 67649372867 scopus 로고    scopus 로고
    • Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators
    • Elsevier, New York
    • N. Kopell and G. B. Ermentrout, Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators, in Handbook of Dynamical Systems: Toward Applications, Vol. 2, Elsevier, New York, 2002, pp. 3-54.
    • (2002) Handbook of Dynamical Systems: Toward Applications , vol.2 , pp. 3-54
    • Kopell, N.1    Ermentrout, G.B.2
  • 23
    • 7444259575 scopus 로고    scopus 로고
    • Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks
    • N. J. Kopell and B. Ermentrout, Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 15482-15487.
    • (2004) Proc. Natl. Acad. Sci. USA , vol.101 , pp. 15482-15487
    • Kopell, N.J.1    Ermentrout, B.2
  • 24
    • 84877083069 scopus 로고    scopus 로고
    • Phase resetting reduces theta-gamma rhythmic interaction to a onedimensional map
    • P. Malerba and N. Kopell, Phase resetting reduces theta-gamma rhythmic interaction to a onedimensional map, J. Math. Biol., 66 (2013), pp. 1361-1386.
    • (2013) J. Math. Biol , vol.66 , pp. 1361-1386
    • Malerba, P.1    Kopell, N.2
  • 25
    • 13844299470 scopus 로고    scopus 로고
    • The combined effects of inhibitory and electrical synapses in synchrony
    • B. Pfeuty, D. G. G. Mato, and D. Hansel, The combined effects of inhibitory and electrical synapses in synchrony, Neural Comput., 17 (2005), pp. 633-670.
    • (2005) Neural Comput , vol.17 , pp. 633-670
    • Pfeuty, B.1    Mato, D.G.G.2    Hansel, D.3
  • 27
    • 0030155390 scopus 로고    scopus 로고
    • Regulation of gap junction coupling in the developing neocortex
    • B. Rorig and B. Sutor, Regulation of gap junction coupling in the developing neocortex, Mol. Neurobiol., 12 (1996), pp. 225-249.
    • (1996) Mol. Neurobiol , vol.12 , pp. 225-249
    • Rorig, B.1    Sutor, B.2
  • 28
    • 67649321652 scopus 로고    scopus 로고
    • Geometric singular perturbation analysis of neuronal dynamics
    • Elsevier, New York
    • J. E. Rubin and D. Terman, Geometric singular perturbation analysis of neuronal dynamics, in Handbook of Dynamical Systems: Toward Applications, Vol. 2, Elsevier, New York, 2002, pp. 93-146.
    • (2002) Handbook of Dynamical Systems: Toward Applications , vol.2 , pp. 93-146
    • Rubin, J.E.1    Terman, D.2
  • 29
    • 84884932935 scopus 로고    scopus 로고
    • Dynamic mechanisms in networks of interneurons with periodic drives
    • Ph.D. thesis, , Center for BioDynamics, Boston University, Boston, MA
    • A. K. Serenevy, Dynamic Mechanisms in Networks of Interneurons with Periodic Drives, Ph.D. thesis, Department of Mathematics and Statistics, Center for BioDynamics, Boston University, Boston, MA, 2007.
    • (2007) Department of Mathematics and Statistics
    • Serenevy, A.K.1
  • 30
    • 0028457504 scopus 로고
    • Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks
    • F. K. Skinner, N. Kopell, and E. Marder, Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks, J. Comput. Neurosci., 1 (1994), pp. 69-87.
    • (1994) J. Comput. Neurosci , vol.1 , pp. 69-87
    • Skinner, F.K.1    Kopell, N.2    Marder, E.3
  • 31
    • 0000821114 scopus 로고    scopus 로고
    • Dynamics of two mutually coupled slow inhibitory neurons
    • D. Terman, A. Bose, and N. Kopell, Dynamics of two mutually coupled slow inhibitory neurons, Phys. D, 117 (1998), pp. 241-275.
    • (1998) Phys. D , vol.117 , pp. 241-275
    • Terman, D.1    Bose, A.2    Kopell, N.3
  • 32
  • 33
    • 47549103136 scopus 로고    scopus 로고
    • Modeling GABA alterations in schizophrenia: A link between impaired inhibition and altered gamma and beta range auditory entrainment
    • D. Vierling-Claassen, P. Siekmeier, S. Stufflebeam, and N. Kopell, Modeling GABA alterations in schizophrenia: A link between impaired inhibition and altered gamma and beta range auditory entrainment, J. Neurophysiol., 99 (2008), pp. 2656-2671.
    • (2008) J. Neurophysiol , vol.99 , pp. 2656-2671
    • Vierling-Claassen, D.1    Siekmeier, P.2    Stufflebeam, S.3    Kopell, N.4
  • 34
    • 0029836487 scopus 로고    scopus 로고
    • Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model
    • X. J. Wang and G. Buzsaki, Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model, J. Neurosci., 16 (1996), pp. 6402-6413.
    • (1996) J. Neurosci , vol.16 , pp. 6402-6413
    • Wang, X.J.1    Buzsaki, G.2
  • 35
    • 0003082358 scopus 로고
    • Alternating and synchronous rhythms in reciprocally inhibitory model neurons
    • X. J. Wang and J. Rinzel, Alternating and synchronous rhythms in reciprocally inhibitory model neurons, Neural Comput., 4 (1992), pp. 84-97.
    • (1992) Neural Comput , vol.4 , pp. 84-97
    • Wang, X.J.1    Rinzel, J.2
  • 36
    • 0027193370 scopus 로고
    • Spindle rhythmicity in the reticularis thalami nucleus: Synchronization among mutually inhibitory neurons
    • X. J. Wang and J. Rinzel, Spindle rhythmicity in the reticularis thalami nucleus: Synchronization among mutually inhibitory neurons, Neurosci., 53 (1993), pp. 899-904.
    • (1993) Neurosci , vol.53 , pp. 899-904
    • Wang, X.J.1    Rinzel, J.2
  • 37
    • 0034608872 scopus 로고    scopus 로고
    • Networks of interneurons with fast and slow ?-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-Theta rhythm
    • J. A. White, M. I. Banks, R. A. Pearce, and N. J. Kopell, Networks of interneurons with fast and slow ?-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gamma-Theta rhythm, Proc. Natl. Acad. Sci. USA, 97 (2000), pp. 8128-8133.
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 8128-8133
    • White, J.A.1    Banks, M.I.2    Pearce, R.A.3    Kopell, N.J.4
  • 38
    • 0031881939 scopus 로고    scopus 로고
    • Synchronization and oscillatory dynamics in heterogeneous mutually inhibited neurons
    • J. A. White, C. C. Chow, J. Ritt, C. Soto-Trevino, and N. Kopell, Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons, J. Comput. Neurosci., 5 (1998), pp. 5-16.
    • (1998) J. Comput. Neurosci , vol.5 , pp. 5-16
    • White, J.A.1    Chow, C.C.2    Ritt, J.3    Soto-Trevino, C.4    Kopell, N.5
  • 39
    • 0033705948 scopus 로고    scopus 로고
    • Inhibition-based rhythms: Experimental and mathematical observations on network dynamics
    • M. Whittington, R. D. Traub, N. Kopell, B. Ermentrout, and E. H. Buhl, Inhibition-based rhythms: Experimental and mathematical observations on network dynamics, Int. J. Psychophysiol., 38 (2000), pp. 315-336.
    • (2000) Int. J. Psychophysiol , vol.38 , pp. 315-336
    • Whittington, M.1    Traub, R.D.2    Kopell, N.3    Ermentrout, B.4    Buhl, E.H.5
  • 40
    • 0028985211 scopus 로고
    • Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation
    • M. A. Whittington, R. D. Traub, and J. G. Jeffreys, Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation, Nature, 373 (1995), pp. 612-615.
    • (1995) Nature , vol.373 , pp. 612-615
    • Whittington, M.A.1    Traub, R.D.2    Jeffreys, J.G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.