메뉴 건너뛰기




Volumn 8, Issue 1, 2009, Pages 253-278

Canards, clusters, and synchronization in a weakly coupled interneuron model

Author keywords

Canards; Clusters; Neurons; Synchrony; Weak coupling

Indexed keywords

BIOPHYSICAL MODELS; CANARDS; CLUSTERS; COMPLEX DYNAMICS; COUPLED OSCILLATORS; GAP JUNCTIONS; INHIBITORY INTERNEURONS; LARGE NETWORKS; LOW CURRENTS; MIXED-MODE OSCILLATIONS; POTASSIUM CURRENTS; REDUCED MODELS; SUB THRESHOLDS; SYNCHRONY; THREE DIMENSIONS; TIGHT JUNCTIONS; TIME-SCALE; WEAK COUPLING;

EID: 63049107517     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/080724010     Document Type: Article
Times cited : (61)

References (52)
  • 1
    • 34249831818 scopus 로고
    • The dynamics of n weakly coupled oscillators
    • P. ASHWIN AND J. W. SWIFT, The dynamics of n weakly coupled oscillators, J. Nonlinear Sci., 2 (1992), pp. 69-108.
    • (1992) J. Nonlinear Sci , vol.2 , pp. 69-108
    • ASHWIN, P.1    SWIFT, J.W.2
  • 2
    • 41549159259 scopus 로고    scopus 로고
    • Mixed-mode oscillations and cluster patterns in an electrochemical relaxation oscillator under galvanostatic control
    • N. BABA AND K. KRISCHER, Mixed-mode oscillations and cluster patterns in an electrochemical relaxation oscillator under galvanostatic control, Chaos, 18 (2008), 015103.
    • (2008) Chaos , vol.18 , pp. 015103
    • BABA, N.1    KRISCHER, K.2
  • 3
    • 0036763360 scopus 로고    scopus 로고
    • Clustering in globally coupled oscillators
    • M. BANAJI, Clustering in globally coupled oscillators, Dynamical Systems, 17 (2002), pp. 263-285.
    • (2002) Dynamical Systems , vol.17 , pp. 263-285
    • BANAJI, M.1
  • 4
    • 0001031806 scopus 로고
    • Third Schnepfenried Geometry Conference Astérisque 109-110, Soc. Math. France, Paris
    • 3 et leur canards, in Third Schnepfenried Geometry Conference Vol. 2, Astérisque 109-110, Soc. Math. France, Paris, 1983, pp. 159-191.
    • (1983) 3 et leur canards , vol.2 , pp. 159-191
    • BENOIT, E.1
  • 6
    • 41549110987 scopus 로고    scopus 로고
    • Introduction to focus issue: Mixed mode sscillations: Experiment, computation, and analysis
    • M. BRØNS, T. KAPER, AND H. ROTSTEIN, Introduction to focus issue: Mixed mode sscillations: Experiment, computation, and analysis, Chaos, 18 (2008), 015101.
    • (2008) Chaos , vol.18 , pp. 015101
    • BRØNS, M.1    KAPER, T.2    ROTSTEIN, H.3
  • 7
    • 84869247534 scopus 로고    scopus 로고
    • M. BRØNS, M. KRUPA, AND M. WECHSELBER. GER, Mixed mode oscillations due to the generalized canard phenomenon, in Bifurcation Theory and Spatio-temporal Pattern Formation, Fields Inst. Commun. 49, AMS, Providence, RI, 2006, pp. 39-63.
    • M. BRØNS, M. KRUPA, AND M. WECHSELBER. GER, Mixed mode oscillations due to the generalized canard phenomenon, in Bifurcation Theory and Spatio-temporal Pattern Formation, Fields Inst. Commun. 49, AMS, Providence, RI, 2006, pp. 39-63.
  • 9
    • 0034223131 scopus 로고    scopus 로고
    • Dynamics of spiking neurons with electrical coupling
    • C. C CHOW AND N. KOPELL, Dynamics of spiking neurons with electrical coupling, Neural Comput., 12 (2000), pp. 1643-1678.
    • (2000) Neural Comput , vol.12 , pp. 1643-1678
    • CHOW, C.C.1    KOPELL, N.2
  • 11
    • 4344624410 scopus 로고    scopus 로고
    • Chaotic spiking in the Hodgkin Huxley nerve model with slow inactivation of the sodium current
    • S. DOI, J. INOUE, AND S. KUMAGAI, Chaotic spiking in the Hodgkin Huxley nerve model with slow inactivation of the sodium current, J. Integr. Neurosci., 3 (2004), pp. 207-225.
    • (2004) J. Integr. Neurosci , vol.3 , pp. 207-225
    • DOI, S.1    INOUE, J.2    KUMAGAI, S.3
  • 12
    • 16244415882 scopus 로고    scopus 로고
    • Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies
    • J. DROVER, J. RUBIN, J. SU, AND B. ERMENTROUT, Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies, SIAM J. Appl. Math., 65 (2004), pp. 69-92.
    • (2004) SIAM J. Appl. Math , vol.65 , pp. 69-92
    • DROVER, J.1    RUBIN, J.2    SU, J.3    ERMENTROUT, B.4
  • 13
    • 0032738083 scopus 로고    scopus 로고
    • Function of specific K+ channels in sustained high-frequency firing of fast-spiking neocortical cells
    • A. ERISIR., D. LAU, B. RUDY, AND S. LEONARD, Function of specific K+ channels in sustained high-frequency firing of fast-spiking neocortical cells, J. Neurophysiol., 82 (1999), pp. 2476-2489.
    • (1999) J. Neurophysiol , vol.82 , pp. 2476-2489
    • ERISIR, A.1    LAU, D.2    RUDY, B.3    LEONARD, S.4
  • 14
    • 0000747853 scopus 로고
    • Frequency plateaus in a chain of weakly coupled oscillators
    • G. B. ERMENTROUT AND N. KOPELL, Frequency plateaus in a chain of weakly coupled oscillators, I., SIAM J. Math. Anal, 15 (1984), pp. 215-237.
    • (1984) I., SIAM J. Math. Anal , vol.15 , pp. 215-237
    • ERMENTROUT, G.B.1    KOPELL, N.2
  • 15
    • 33749329257 scopus 로고    scopus 로고
    • Gap junctions destroy persistent states in excitatory networks
    • B. ERMENTROUT, Gap junctions destroy persistent states in excitatory networks, Phys. Rev. E (3), 74 (2006), 031918.
    • (2006) Phys. Rev. E , vol.74 , Issue.3 , pp. 031918
    • ERMENTROUT, B.1
  • 16
    • 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
  • 17
    • 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
    • 14844324709 scopus 로고    scopus 로고
    • Functional properties of electrical synapses between inhibitory interneurons of neocortical layer 4
    • J. R. GIBSON, M. BEIERLEIN, AND B. W. CONNORS, Functional properties of electrical synapses between inhibitory interneurons of neocortical layer 4, J. Neurophysiol., 93 (2005), pp. 467-480.
    • (2005) J. Neurophysiol , vol.93 , pp. 467-480
    • GIBSON, J.R.1    BEIERLEIN, M.2    CONNORS, B.W.3
  • 19
    • 33745981128 scopus 로고
    • Clustering in globally coupled phase oscillators
    • D. GOLOMB, D. HANSEL, B. SHRAIMAN, AND H. SOMPOLINSKY, Clustering in globally coupled phase oscillators, Phys. Rev. A, 45 (1992), pp. 3516-3530.
    • (1992) Phys. Rev. A , vol.45 , pp. 3516-3530
    • GOLOMB, D.1    HANSEL, D.2    SHRAIMAN, B.3    SOMPOLINSKY, H.4
  • 20
    • 34548409170 scopus 로고    scopus 로고
    • D. GOLOMB, K. DONNER, L. SHACHAM, D. SHLOSBER.G, Y. AMITAI, AND D. HANSEL, Mechanisms of firing patterns in fast-spiking cortical interneurons, PLoS. Comput. Biol., 3 (8) (2007), e156.
    • D. GOLOMB, K. DONNER, L. SHACHAM, D. SHLOSBER.G, Y. AMITAI, AND D. HANSEL, Mechanisms of firing patterns in fast-spiking cortical interneurons, PLoS. Comput. Biol., 3 (8) (2007), e156.
  • 21
    • 33846461739 scopus 로고    scopus 로고
    • Response properties and synchronization of rhythmically firing dendritic neurons
    • J. A. GOLDBERG, C. A. DEISTER, AND C. J. WILSON, Response properties and synchronization of rhythmically firing dendritic neurons, J. Neurophysiol., 97 (2007), pp. 208-219.
    • (2007) J. Neurophysiol , vol.97 , pp. 208-219
    • GOLDBERG, J.A.1    DEISTER, C.A.2    WILSON, C.J.3
  • 22
  • 24
    • 41549138692 scopus 로고    scopus 로고
    • Return maps of folded nodes and folded saddle-nodes
    • J. GUCKENHEIMER, Return maps of folded nodes and folded saddle-nodes, Chaos, 18 (2008), 015108.
    • (2008) Chaos , vol.18 , pp. 015108
    • GUCKENHEIMER, J.1
  • 25
    • 56449117107 scopus 로고    scopus 로고
    • Singular Hopf bifurcation in systems with two slow variables
    • J. GUCKENHEIMER, Singular Hopf bifurcation in systems with two slow variables, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 1355-1377.
    • (2008) SIAM J. Appl. Dyn. Syst , vol.7 , pp. 1355-1377
    • GUCKENHEIMER, J.1
  • 26
    • 57249105481 scopus 로고    scopus 로고
    • F. GÜR.EL KAZANCI AND G. B. ERMENTROUT, Wave formation through the interactions between clustered states and local coupling in arrays of neural oscillators, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 491-509.
    • F. GÜR.EL KAZANCI AND G. B. ERMENTROUT, Wave formation through the interactions between clustered states and local coupling in arrays of neural oscillators, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 491-509.
  • 27
    • 23044468737 scopus 로고    scopus 로고
    • Phase-response curves give the responses of neurons to transient inputs
    • B. S. GUTKIN, G. B. ERMENTROUT, AND A. D. REYES, Phase-response curves give the responses of neurons to transient inputs, J. Neurophysiol., 94 (2005), pp. 1623-1635.
    • (2005) J. Neurophysiol , vol.94 , pp. 1623-1635
    • GUTKIN, B.S.1    ERMENTROUT, G.B.2    REYES, A.D.3
  • 28
    • 33751516522 scopus 로고
    • Clustering and slow switching in globally coupled phase oscillators
    • D. HANSEL, G. MATO, AND C MEUNIER, Clustering and slow switching in globally coupled phase oscillators, Phys. Rev. E, 48 (1993), pp. 3470-3477.
    • (1993) Phys. Rev. E , vol.48 , pp. 3470-3477
    • HANSEL, D.1    MATO, G.2    MEUNIER, C.3
  • 29
    • 0029258143 scopus 로고
    • Synchrony in excitatory neural networks
    • D. HANSEL, G. MATO, AND C. MEUNIER., Synchrony in excitatory neural networks, Neural Comput., 7 (1995), pp. 307-337.
    • (1995) Neural Comput , vol.7 , pp. 307-337
    • HANSEL, D.1    MATO, G.2    MEUNIER, C.3
  • 30
    • 0035359894 scopus 로고    scopus 로고
    • Synchronization of elliptic bursters
    • E. M. IZHIKEVICH, Synchronization of elliptic bursters, SIAM Rev., 43 (2001), pp. 315-344.
    • (2001) SIAM Rev , vol.43 , pp. 315-344
    • IZHIKEVICH, E.M.1
  • 32
    • 33847644102 scopus 로고    scopus 로고
    • Synchrony of neuronal oscillations controlled by GAB Aergic reversal potentials
    • H. Y. JEONG AND B. GUTKIN, Synchrony of neuronal oscillations controlled by GAB Aergic reversal potentials, Neural Comput., 19 (2007), pp. 706-729.
    • (2007) Neural Comput , vol.19 , pp. 706-729
    • JEONG, H.Y.1    GUTKIN, B.2
  • 33
    • 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
  • 34
    • 41549122782 scopus 로고    scopus 로고
    • Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron
    • M. KRUPA, N. POPOVIC, N. KOPELL, AND H. ROTSTEIN, Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron, Chaos, 18 (2008), 015106.
    • (2008) Chaos , vol.18 , pp. 015106
    • KRUPA, M.1    POPOVIC, N.2    KOPELL, N.3    ROTSTEIN, H.4
  • 37
    • 0038701723 scopus 로고    scopus 로고
    • Dynamics of spiking neurons connected by both inhibitory and electrical coupling
    • T. J. LEWIS AND J. RINZEL, Dynamics of spiking neurons connected by both inhibitory and electrical coupling, J. Comput. Neurosci., 14 (2003), pp. 283-309.
    • (2003) J. Comput. Neurosci , vol.14 , pp. 283-309
    • LEWIS, T.J.1    RINZEL, J.2
  • 38
    • 33847229047 scopus 로고    scopus 로고
    • Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex
    • J. G. MANCILLA, T. J. LEWIS, D. J. PINTO, J. RINZEL, AND B. W. CONNORS, Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex, J. Neurosci., 27 (2007), pp. 2058-2073.
    • (2007) J. Neurosci , vol.27 , pp. 2058-2073
    • MANCILLA, J.G.1    LEWIS, T.J.2    PINTO, D.J.3    RINZEL, J.4    CONNORS, B.W.5
  • 40
    • 0041324860 scopus 로고    scopus 로고
    • Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses
    • M. NOMURA, T. FUKAI, AND T. AOYAGI, Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses, Neural Comput., 15 (2003), pp. 2179-2198.
    • (2003) Neural Comput , vol.15 , pp. 2179-2198
    • NOMURA, M.1    FUKAI, T.2    AOYAGI, T.3
  • 41
    • 13844299470 scopus 로고    scopus 로고
    • The combined effects of inhibitory and electrical synapses in synchrony
    • B. PFEUTY, G. MATO, D. GOLOMB, 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, G.2    GOLOMB, D.3    HANSEL, D.4
  • 42
    • 33749533590 scopus 로고    scopus 로고
    • The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells
    • H. ROTSTEIN, T. OPPERMAN, J. WHITE, AND N. KOPELL, The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells, J. Comput. Neurosci., 21 (2006), pp. 271-292.
    • (2006) J. Comput. Neurosci , vol.21 , pp. 271-292
    • ROTSTEIN, H.1    OPPERMAN, T.2    WHITE, J.3    KOPELL, N.4
  • 43
    • 63049099934 scopus 로고    scopus 로고
    • Canard induced mixed-mode oscillations in a medial entorhinal cortex layer IT stellate cell model
    • H. G. ROTSTEIN, M. WECHSELBERGER, AND N. KOPELL, Canard induced mixed-mode oscillations in a medial entorhinal cortex layer IT stellate cell model, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 1582-1611.
    • (2008) SIAM J. Appl. Dyn. Syst , vol.7 , pp. 1582-1611
    • ROTSTEIN, H.G.1    WECHSELBERGER, M.2    KOPELL, N.3
  • 44
    • 34547379404 scopus 로고    scopus 로고
    • Giant squid-hidden canard: The 3D geometry of the Hodgkin Huxley model
    • J. RUBIN AND M. WECHSELBERGER, Giant squid-hidden canard: The 3D geometry of the Hodgkin Huxley model, Biol. Cybernet., 97 (2007), pp. 5-32.
    • (2007) Biol. Cybernet , vol.97 , pp. 5-32
    • RUBIN, J.1    WECHSELBERGER, M.2
  • 45
    • 41549101374 scopus 로고    scopus 로고
    • The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales
    • J. RUBIN AND M. WECHSELBERGER, The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales, Chaos, 18 (2008), 015105.
    • (2008) Chaos , vol.18 , pp. 015105
    • RUBIN, J.1    WECHSELBERGER, M.2
  • 47
    • 19744369589 scopus 로고    scopus 로고
    • Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators
    • J. TERAMAE AND D. TANAKA, Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators, Phys. Rev. Lett., 93 (2004), 204103.
    • (2004) Phys. Rev. Lett , vol.93 , pp. 204103
    • TERAMAE, J.1    TANAKA, D.2
  • 48
  • 49
    • 0029836487 scopus 로고    scopus 로고
    • Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model
    • X. J. WANG AND G. BUSZAKI, 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    BUSZAKI, G.2
  • 52
    • 0031881939 scopus 로고    scopus 로고
    • Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons
    • J. A. WHITE, C. C. CHOW, J. RITT, C SOTO-TREVIO, 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-TREVIO, C.4    KOPELL, N.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.