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Volumn 56, Issue 3, 2008, Pages 311-345

A discrete time neural network model with spiking neurons : RRRigorous results on the spontaneous dynamics

Author keywords

Dynamical systems; Neural networks; Symbolic coding

Indexed keywords

ACTION POTENTIAL; ALGORITHM; ARTICLE; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; LONG TERM DEPRESSION; LONG TERM POTENTIATION; NERVE CELL; NERVE CELL NETWORK; NERVE CELL PLASTICITY; PHYSIOLOGY; PROBABILITY; SYNAPSE; SYNAPTIC TRANSMISSION;

EID: 36749004948     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-007-0117-3     Document Type: Article
Times cited : (60)

References (55)
  • 2
    • 0031184911 scopus 로고    scopus 로고
    • A dynamical system approach to SOC models of Zhang's type
    • Blanchard Ph., Cessac B. and Krüger T. (1997). A dynamical system approach to SOC models of Zhang's type. J. Stat. Phys. 88: 307-318
    • (1997) J. Stat. Phys. , vol.88 , pp. 307-318
    • Blanchard, Ph.1    Cessac, B.2    Krüger, T.3
  • 3
    • 0033633230 scopus 로고    scopus 로고
    • What can one learn about self-organized criticality from dynamical system theory?
    • Blanchard Ph., Cessac B. and Krüger T. (2000). What can one learn about self-organized criticality from dynamical system theory?. J. Stat. Phys. 98: 375-404
    • (2000) J. Stat. Phys. , vol.98 , pp. 375-404
    • Blanchard, Ph.1    Cessac, B.2    Krüger, T.3
  • 5
    • 0033210816 scopus 로고    scopus 로고
    • Fast global oscillations in networks of integrate-and-fire neurons with low firing rates
    • Brunel N. and Hakim V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput. 11: 1621-1671
    • (1999) Neural Comput. , vol.11 , pp. 1621-1671
    • Brunel, N.1    Hakim, V.2
  • 6
    • 0001961264 scopus 로고
    • Mean-field equations, bifurcation map and route to chaos in discrete time neural networks
    • Cessac B., Doyon B., Quoy M. and Samuelides M. (1994). Mean-field equations, bifurcation map and route to chaos in discrete time neural networks. Physica D 74: 24-44
    • (1994) Physica D , vol.74 , pp. 24-44
    • Cessac, B.1    Doyon, B.2    Quoy, M.3    Samuelides, M.4
  • 7
    • 84957330048 scopus 로고
    • Occurence of chaos and at line in random neural networks
    • 8
    • Cessac B. (1994). Occurence of chaos and AT line in random neural networks. Europhys. Lett. 26(8): 577-582
    • (1994) Europhys. Lett. , vol.26 , pp. 577-582
    • Cessac, B.1
  • 8
    • 0000362119 scopus 로고
    • Increase in complexity in random neural networks
    • Cessac B. (1995). Increase in complexity in random neural networks. J. de Physique I (France) 5: 409-432
    • (1995) J. de Physique i (France) , vol.5 , pp. 409-432
    • Cessac, B.1
  • 11
    • 41349089523 scopus 로고    scopus 로고
    • Stable resonances and signal propagation in a chaotic network of coupled units
    • Cessac B. and Sepulchre J.A. (2004). Stable resonances and signal propagation in a chaotic network of coupled units. Phys. Rev. E 70: 056111
    • (2004) Phys. Rev. e , vol.70 , pp. 056111
    • Cessac, B.1    Sepulchre, J.A.2
  • 12
    • 33645679781 scopus 로고    scopus 로고
    • Transmitting a signal by amplitude modulation in a chaotic network
    • Cessac B. and Sepulchre J.A. (2006). Transmitting a signal by amplitude modulation in a chaotic network. Chaos 16: 013104
    • (2006) Chaos , vol.16 , pp. 013104
    • Cessac, B.1    Sepulchre, J.A.2
  • 13
    • 36749084550 scopus 로고    scopus 로고
    • Linear Response in a class of simple systems far from equilibrium
    • Cessac, B., Sepulchre, J.A.: Linear Response in a class of simple systems far from equilibrium. Physica D 225(1): 13-28
    • Physica D , vol.225 , Issue.1 , pp. 13-28
    • Cessac, B.1    Sepulchre, J.A.2
  • 17
    • 33645053513 scopus 로고    scopus 로고
    • Discrete time piecewise affine models of genetic regulatory networks
    • Coutinho R., Fernandez B., Lima R. and Meyroneinc A. (2006). Discrete time piecewise affine models of genetic regulatory networks. J. Math. Biol. 52: 524-570
    • (2006) J. Math. Biol. , vol.52 , pp. 524-570
    • Coutinho, R.1    Fernandez, B.2    Lima, R.3    Meyroneinc, A.4
  • 18
    • 0032053304 scopus 로고    scopus 로고
    • Self- Organization and Dynamics reduction in recurrent networks: Stimulus presentation and learning
    • Dauce E., Quoy M., Cessac B., Doyon B. and Samuelides M. (1998). Self- Organization and Dynamics reduction in recurrent networks: stimulus presentation and learning. Neural Netw 11: 521-533
    • (1998) Neural Netw , vol.11 , pp. 521-533
    • Dauce, E.1    Quoy, M.2    Cessac, B.3    Doyon, B.4    Samuelides, M.5
  • 19
    • 0001444374 scopus 로고
    • Dynamical phaste transition in non-symmetric spin glasses
    • Derrida B. (1987). Dynamical phaste transition in non-symmetric spin glasses. J. Phys. A Math. Gen. 20: 721-725
    • (1987) J. Phys. A Math. Gen. , vol.20 , pp. 721-725
    • Derrida, B.1
  • 20
    • 36149035332 scopus 로고
    • Multivalley structure in Kauffman's model: Analogy with spin glasses
    • Derrida B. and Flyvbjerg H. (1986). Multivalley structure in Kauffman's model: analogy with spin glasses. J. Phys. A19: L1003-L1008
    • (1986) J. Phys. , vol.19
    • Derrida, B.1    Flyvbjerg, H.2
  • 21
    • 84956252965 scopus 로고
    • Random networks of automata: A simple annealed approximation
    • Derrida B. and Pomeau Y. (1986). Random networks of automata: a simple annealed approximation. Europhys. Lett. 1: 45-49
    • (1986) Europhys. Lett. , vol.1 , pp. 45-49
    • Derrida, B.1    Pomeau, Y.2
  • 22
    • 35949018382 scopus 로고
    • Ergodic Theory of Strange attractors
    • Eckmann J.P. and Ruelle D. (1985). Ergodic Theory of Strange attractors. Rev. Mod. Phys. 57: 617
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617
    • Eckmann, J.P.1    Ruelle, D.2
  • 29
    • 77956707015 scopus 로고
    • Current carried by sodium and potassium ions through the membrane of the giant axon of Loligo
    • Hodgkin A.L. and Huxley A.F. (1952). Current carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J. Physiol. (Lond.) 116: 449-472
    • (1952) J. Physiol. (Lond.) , vol.116 , pp. 449-472
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 30
    • 35649001607 scopus 로고
    • A quantitative description of ion currents and its applications to conduction and excitation in nerve membranes
    • Hodgkin A.L. and Huxley A.F. (1952). A quantitative description of ion currents and its applications to conduction and excitation in nerve membranes. J. Physiol. (Lond.) 117: 500-544
    • (1952) J. Physiol. (Lond.) , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 31
    • 84967728280 scopus 로고
    • Prevalence: A translation-invariant 'almost every' on infinite-dimensional spaces
    • Hunt B.R., Sauer T. and Yorke J.A. (1992). Prevalence: a translation-invariant 'almost every' on infinite-dimensional spaces. Bull. Am. Math. Soc. 27: 217-238
    • (1992) Bull. Am. Math. Soc. , vol.27 , pp. 217-238
    • Hunt, B.R.1    Sauer, T.2    Yorke, J.A.3
  • 32
    • 0742268989 scopus 로고    scopus 로고
    • Simple model of spiking neurons
    • Izhikevich E.M. (2003). Simple model of spiking neurons. IEEE Trans Neural Netw 14: 1569-572
    • (2003) IEEE Trans Neural Netw , vol.14 , pp. 1569-572
    • Izhikevich, E.M.1
  • 38
    • 45149138762 scopus 로고
    • Computation at the edge of chaos
    • Langton C.G. (1990). Computation at the edge of chaos. Physica D 42: 12-37
    • (1990) Physica D , vol.42 , pp. 12-37
    • Langton, C.G.1
  • 39
    • 29144511579 scopus 로고    scopus 로고
    • Dynamical complexity of discrete time regulatory networks
    • Lima R. and Ugalde E. (2006). Dynamical complexity of discrete time regulatory networks. Nonlinearity 19: 237-259
    • (2006) Nonlinearity , vol.19 , pp. 237-259
    • Lima, R.1    Ugalde, E.2
  • 42
    • 0001823266 scopus 로고
    • Adaptation towards the edge of chaos
    • Kelso, J.A.S, Mandell, A.J., Shlesinger, M.F. (eds.) World Scientific, Singapore
    • Packard, N.: Adaptation towards the edge of chaos. In: Kelso, J.A.S, Mandell, A.J., Shlesinger, M.F. (eds.) Dynamic Patterns in Complex Systems. pp. 293-301. World Scientific, Singapore (1988)
    • (1988) Dynamic Patterns in Complex Systems , pp. 293-301
    • Packard, N.1
  • 43
    • 0000271607 scopus 로고
    • Zeta functions and the periodic orbit structure of hyperbolic dynamics
    • Société Mathématique de France
    • Parry, W., Pollicott, M.: Zeta functions and the periodic orbit structure of hyperbolic dynamics. Collection Asterisque 187-188, Société Mathématique de France (1990)
    • (1990) Collection Asterisque , vol.187-188
    • Parry, W.1    Pollicott, M.2
  • 45
    • 27744439912 scopus 로고    scopus 로고
    • The role of delays in shaping the spatio-temporal dynamics of neuronal activity in large networks
    • Roxin N.B. and Hansel D. (2005). The role of delays in shaping the spatio-temporal dynamics of neuronal activity in large networks. Phys. Rev. Lett. 94: 238103
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 238103
    • Roxin, N.B.1    Hansel, D.2
  • 46
    • 33748464002 scopus 로고    scopus 로고
    • Analytical integrate and fire neuron models with conductance-based dynamics for event driven simulation strategies
    • Rudolph M. and Destexhe A. (2006). Analytical integrate and fire neuron models with conductance-based dynamics for event driven simulation strategies. Neural Comput. 18: 2146-2210
    • (2006) Neural Comput. , vol.18 , pp. 2146-2210
    • Rudolph, M.1    Destexhe, A.2
  • 47
    • 84956071330 scopus 로고
    • Gibbs measures in ergodic theory
    • 4
    • Sinai Ya.G. (1972). Gibbs measures in ergodic theory. Russ. Math. Surv. 27(4): 21-69
    • (1972) Russ. Math. Surv. , vol.27 , pp. 21-69
    • Sinai, Ya.G.1
  • 49
    • 85009367586 scopus 로고
    • Equilibrium states and the ergodic theory of Anosov diffeomorphisms
    • Springer, Berlin
    • Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lect. Notes. in Math., vol. 470. Springer, Berlin (1975)
    • (1975) Lect. Notes. in Math. , vol.470
    • Bowen, R.1
  • 52
    • 36749100509 scopus 로고    scopus 로고
    • Random recurrent neural Networks
    • review paper, to appear in, topics in neural networks Springer, Heidelberg
    • Samuelides, M., Cessac, B.: Random recurrent neural Networks. review paper, to appear in, topics in neural networks. Eur. Phys. J. (topical issue), Springer, Heidelberg (2006)
    • (2006) Eur. Phys. J. (Topical Issue)
    • Samuelides, M.1    Cessac, B.2
  • 53
    • 33646170322 scopus 로고    scopus 로고
    • Weak pairwise correlations imply strongly correlated network states in a neural population
    • 04701
    • Schneidman, E., Berry, M.J., Segev, R., Bialek, W.: Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 04701, vol. 440 (2006)
    • (2006) Nature , vol.440
    • Schneidman, E.1    Berry, M.J.2    Segev, R.3    Bialek, W.4
  • 55
    • 33644875527 scopus 로고    scopus 로고
    • Spontaneous dynamics of assymmetric random recurrent spiking neural networks
    • Soula H., Beslon G. and Mazet O. (2006). Spontaneous dynamics of assymmetric random recurrent spiking neural networks. Neural Comput. 18: 1
    • (2006) Neural Comput. , vol.18 , pp. 1
    • Soula, H.1    Beslon, G.2    Mazet, O.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.