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Volumn 73, Issue 3, 2013, Pages 1260-1279

Relaxation and self-sustained oscillations in the time elapsed neuron network model

Author keywords

Desynchronization; Neuron networks; Self sust ained oscillations

Indexed keywords

DESYNCHRONIZATION; GENERALIZED RELATIVE ENTROPIES; MATHEMATICAL DESCRIPTIONS; NEURON NETWORKS; NON-LINEAR BOUNDARY CONDITIONS; PROBABILITY DENSITIES; SELF-SUST AINED OSCILLATIONS; WEAKLY CONNECTED NETWORKS;

EID: 84884136684     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/110847962     Document Type: Article
Times cited : (58)

References (29)
  • 1
    • 0032521364 scopus 로고    scopus 로고
    • Refractoriness and neural precision
    • M. J. BERRY AND M. MEISTER, Refractoriness and neural precision, J. Neurosci., 18(1998), pp. 2200-2211. (Pubitemid 28141424)
    • (1998) Journal of Neuroscience , vol.18 , Issue.6 , pp. 2200-2211
    • Berry II, M.J.1    Meister, M.2
  • 2
    • 0028984595 scopus 로고
    • Central control of breathing in mammals: Neuronal circuitry, membrane properties, and neurotransmitters
    • A. L. BIANCHI, M. DENAVIT-SAUBI, AND J. CHAMPAGNAT, Central control of breathing in mammals: Neuronal circuitry, membrane properties, and neurotransmitters, Physiol. Rev., 75(1995), pp. 1-45.
    • (1995) Physiol. Rev. , vol.75 , pp. 1-45
    • Bianchi, A.L.1    Denavit-Saubi, M.2    Champagnat, J.3
  • 3
    • 72849106974 scopus 로고    scopus 로고
    • Mechanisms underlying spontaneous patterned activity in developing neural circuits
    • A. G. BLANKENSHIP AND M. B. FELLER, Mechanisms underlying spontaneous patterned activity in developing neural circuits, Nature Rev. Neurosci., 11(2010), pp. 18-29.
    • (2010) Nature Rev. Neurosci. , vol.11 , pp. 18-29
    • Blankenship, A.G.1    Feller, M.B.2
  • 4
    • 10244241405 scopus 로고    scopus 로고
    • Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes for Sources
    • Birkhäuser Verlag, Basel
    • F. BOUCHUT, Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes for Sources, Front. Math., Birkhäuser Verlag, Basel, 2004.
    • (2004) Front. Math.
    • Bouchut, F.1
  • 5
    • 0033210816 scopus 로고    scopus 로고
    • Fast global oscillations in networks of integrate-and-fire neurons with low firing rates
    • N. BRUNEL AND V. HAKIM, Fast global oscillations in networks of integrate-and-fire neurons with low firing rates, Neural Comput., 11(1999), pp. 1621-1671.
    • (1999) Neural Comput. , vol.11 , pp. 1621-1671
    • Brunel, N.1    Hakim, V.2
  • 6
    • 84861627504 scopus 로고    scopus 로고
    • Analysis of nonlinear noisy integrate & fire neuron models: Blow-up and steady states
    • M. J. CACERES, J. A. CARRILLO, AND B. PERTHAME, Analysis of nonlinear noisy integrate & fire neuron models: Blow-up and steady states, J. Math. Neurosci., 1 (2011).
    • (2011) J. Math. Neurosci. , pp. 1
    • Caceres, M.J.1    Carrillo, J.A.2    Perthame, B.3
  • 7
    • 36048990354 scopus 로고    scopus 로고
    • Coherence resonance and noise-induced synchronization in Hindmarsh Rose neural network with different topologies
    • W. DU-QU AND L. XIAO-SHU, Coherence resonance and noise-induced synchronization in Hindmarsh Rose neural network with different topologies, Commun. Theor. Phys. (Beijing), 48(2007), pp. 759-762.
    • (2007) Commun. Theor. Phys. (Beijing) , vol.48 , pp. 759-762
    • Du-Qu, W.1    Xiao-Shu, L.2
  • 8
    • 0004017463 scopus 로고    scopus 로고
    • Single Neurons, Populations, Plasticity, Cambridge University Press, Cambridge
    • W. GERSTNER AND W. KISTLER, Spiking Neuron Models (Single Neurons, Populations, Plasticity), Cambridge University Press, Cambridge, 2002.
    • (2002) Spiking Neuron Models
    • Gerstner, W.1    Kistler, W.2
  • 9
    • 84871595606 scopus 로고    scopus 로고
    • Transitions in active rotator systems: Invariant hyperbolic manifold approach
    • G. GIACOMIN, K. PAKDAMAN, X. PELLEGRIN, AND C. POQUET, Transitions in active rotator systems: Invariant hyperbolic manifold approach, SIAM J. Math. Anal., 44(2012), pp. 4165-4194.
    • (2012) SIAM J. Math. Anal. , vol.44 , pp. 4165-4194
    • Giacomin, G.1    Pakdaman, K.2    Pellegrin, X.3    Poquet, C.4
  • 10
    • 85114329546 scopus 로고    scopus 로고
    • Numerical Approximation of Hyperbolic Systems of Conservation Laws
    • Springer-Verlag, New York
    • E. GODLEWSKI AND P.-A. RAVIART, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Appl. Math. Sci. 118, Springer-Verlag, New York, 1996.
    • (1996) Appl. Math. Sci. , vol.118
    • Godlewski, E.1    Raviart, P.-A.2
  • 12
    • 34249788999 scopus 로고    scopus 로고
    • State-dependent delays associated to threshold phenomena in structured population dynamics
    • M. L. HBID, E. SANCHEZ, AND R. BRAVO DE LA PARRA, State-dependent delays associated to threshold phenomena in structured population dynamics, Math. Models Methods Appl. Sci., 17(2007), pp. 877-900.
    • (2007) Math. Models Methods Appl. Sci. , vol.17 , pp. 877-900
    • Hbid, M.L.1    Sanchez, E.2    Bravo De La Parra, R.3
  • 14
    • 3142769745 scopus 로고    scopus 로고
    • Respiratory-like rhythmic activity can be produced by an excitatory network of non-pacemaker neuron models
    • DOI 10.1152/jn.00046.2004
    • E. K. KOSMIDIS, O. PIERREFICHE, AND J.-F. VIBERT, Respiratory-like rhythmic activity can be produced by an excitatory network of non-pacemaker neuron models, J. Neurophysiol., 92(2004), pp. 686-699. (Pubitemid 38937043)
    • (2004) Journal of Neurophysiology , vol.92 , Issue.2 , pp. 686-699
    • Kosmidis, E.K.1    Pierrefiche, O.2    Vibert, J.-F.3
  • 15
    • 0016259343 scopus 로고
    • Computer simulation of rhythmic oscillations in neuron pools
    • R. J. MACGREGOR AND R. L. PALASEK, Computer simulation of rhythmic oscillations in neuron pools, Biol. Cybernet., 16(1972), pp. 79-86.
    • (1972) Biol. Cybernet. , vol.16 , pp. 79-86
    • MacGregor, R.J.1    Palasek, R.L.2
  • 16
    • 0003157238 scopus 로고
    • The Dynamics of Physiologically Structured Populations
    • Springer-Verlag, Berlin
    • J. A. J. METZ AND O. DIEKMANN, The Dynamics of Physiologically Structured Populations, Lect. Notes Biomath. 68, Springer-Verlag, Berlin, 1986.
    • (1986) Lect. Notes Biomath. , vol.68
    • Metz, J.A.J.1    Diekmann, O.2
  • 17
    • 24044522878 scopus 로고    scopus 로고
    • General relative entropy inequality: An illustration on growth models
    • DOI 10.1016/j.matpur.2005.04.001, PII S0021782405000528
    • P. MICHEL, S. MISCHLER, AND B. PERTHAME, General relative entropy inequality: An illustration on growth models, J. Math. Pures Appl. (9), 84(2005), pp. 1235-1260. (Pubitemid 41213693)
    • (2005) Journal des Mathematiques Pures et Appliquees , vol.84 , Issue.9 , pp. 1235-1260
    • Michel, P.1    Mischler, S.2    Perthame, B.3
  • 18
    • 21244479396 scopus 로고    scopus 로고
    • Ion channel development, spontaneous activity, and activity-dependent development in nerve and muscle cells
    • DOI 10.1152/physrev.00017.2004
    • W. J. MOODY AND M. M. BOSMA, Ion channel development, spontaneous activity, and activity dependent development in nerve and muscle cells, Physiol. Rev., 85(2005), pp. 883-941. (Pubitemid 40885219)
    • (2005) Physiological Reviews , vol.85 , Issue.3 , pp. 883-941
    • Moody, W.J.1    Bosma, M.M.2
  • 19
    • 76149134681 scopus 로고    scopus 로고
    • Dynamics of a structured neuron population
    • K. PAKDAMAN, B. PERTHAME, AND D. SALORT, Dynamics of a structured neuron population, Nonlinearity, 23(2010), pp. 55-75.
    • (2010) Nonlinearity , vol.23 , pp. 55-75
    • Pakdaman, K.1    Perthame, B.2    Salort, D.3
  • 20
    • 0017227520 scopus 로고
    • A computer program for simulating a network of interacting neurons. I. Organization and physiological assumptions
    • D. H. PERKEL, A computer program for simulating a network of interacting neurons. I. Organization and physiological assumptions, Comput. Biomed. Res., 9(1976), pp. 31-43.
    • (1976) Comput. Biomed. Res. , vol.9 , pp. 31-43
    • Perkel, D.H.1
  • 21
    • 0017226732 scopus 로고
    • A computer program for simulating a network of interacting neurons. III. Applications
    • D. H. PERKEL, A computer program for simulating a network of interacting neurons. III. Applications, Comput. Biomed. Res., 9(1976), pp. 67-74.
    • (1976) Comput. Biomed. Res. , vol.9 , pp. 67-74
    • Perkel, D.H.1
  • 22
    • 0017249047 scopus 로고
    • A computer program for simulating a network of interacting neurons. II. Programming aspects
    • D. H. PERKEL AND M. S. SMITH, A computer program for simulating a network of interacting neurons. II. Programming aspects, Comput. Biomed. Res., 9(1976), pp. 45-66.
    • (1976) Comput. Biomed. Res. , vol.9 , pp. 45-66
    • Perkel, D.H.1    Smith, M.S.2
  • 23
    • 36249025671 scopus 로고    scopus 로고
    • Transport Equations in Biology
    • Birkhäuser, Basel
    • B. PERTHAME, Transport Equations in Biology, Front. Math., Birkhäuser, Basel, 2007.
    • (2007) Front. Math.
    • Perthame, B.1
  • 24
    • 0032053324 scopus 로고    scopus 로고
    • Activity in sparsely connected excitatory neural networks: Effect of connectivity
    • DOI 10.1016/S0893-6080(97)00153-6, PII S0893608097001536
    • J. PHAM, K. PAKDAMAN, J. CHAMPAGNAT, AND J.-F. VIBERT, Activity in sparsely connected excitatory neural networks: Effect of connectivity, Neural Netw., 11(1998), pp. 415-434. (Pubitemid 28351079)
    • (1998) Neural Networks , vol.11 , Issue.3 , pp. 415-434
    • Pham, J.1    Pakdaman, K.2    Champagnat, J.3    Vibert, J.-F.4
  • 25
    • 0032159698 scopus 로고    scopus 로고
    • Noise-induced coherent oscillations in randomly connected neural networks
    • J. PHAM, K. PAKDAMAN, AND J.-F. VIBERT, Noise-induced coherent oscillations in randomly connected neural networks, Phys. Rev. E, 58(1998), pp. 415-434.
    • (1998) Phys. Rev. E , vol.58 , pp. 415-434
    • Pham, J.1    Pakdaman, K.2    Vibert, J.-F.3
  • 26
    • 42449108706 scopus 로고    scopus 로고
    • Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train
    • A. V. RANGAN, G. KOVAČIČ, AND D. CAI, Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train, Phys. Rev. E, 77(2008), 041915.
    • (2008) Phys. Rev. E , vol.77 , pp. 041915
    • Rangan, A.V.1    Kovačič, G.2    Cai, D.3
  • 27
    • 0001723799 scopus 로고
    • Phase transitions in active rotator systems
    • S. SHINOMOTO AND Y. KURAMOTO, Phase transitions in active rotator systems, Prog. Theoret. Phys., 75(1986), pp. 1105-1110.
    • (1986) Prog. Theoret. Phys. , vol.75 , pp. 1105-1110
    • Shinomoto, S.1    Kuramoto, Y.2
  • 28
    • 0037271188 scopus 로고    scopus 로고
    • System size coherence resonance in coupled FitzHugh-Nagumo models
    • DOI 10.1209/epl/i2003-00207-5
    • R. TORAL, C. MIRASSO, AND J. D. GUNTON, System size coherence resonance in coupled FitzHugh-Nagumo models, Europhys. Lett., 61(2003), pp. 162-167. (Pubitemid 36185147)
    • (2003) Europhysics Letters , vol.61 , Issue.2 , pp. 162-167
    • Toral, R.1    Mirasso, C.R.2    Gunton, J.D.3
  • 29
    • 0033754083 scopus 로고    scopus 로고
    • Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons
    • Y. WANG, D. T. W. CHIK, AND Z. D. WANG, Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons, Phys. Rev. E, 61(2000), pp. 740-746.
    • (2000) Phys. Rev. E , vol.61 , pp. 740-746
    • Wang, Y.1    Chik, D.T.W.2    Wang, Z.D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.