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Cebulla C (2007) Asymptotic behavior and synchronizability characteristics of a class of recurrent neural networks. Neural Comput 19:2492-514 [PubMed]

References and models cited by this paper

References and models that cite this paper

Albeverio S, Tirozzi B (1997) An introduction to the mathematical theory of neural networks Fourth Granada Lectures in Computational Physics , Garrido PL:Marro J, ed. pp.197

Allouche JP, Courbage M, Skordev G (2001) Notes on cellular automata Cubo, Matematica Educacional 3:213-244

Anderson JA (1995) An introduction to neural networks

Antonelli F, Dias APS, Golubitsky M, Wang Y (2005) Patterns of synchrony in lattice dynamical systems Nonlinearity 18:2193-2009

Bagnoli F, Cecconi F, Flammini A, Vespignani A (2003) Short period attractors and non-ergodic behavior in the deterministic fixed energy sand pile model Europhysics Letters 63:512-518

Bak P, Tang C, Wiesenfeld K (1988) Self-organized criticality. Phys Rev A Gen Phys 38:364-374 [PubMed]

Barabasi AL, Albert R (1999) Emergence of scaling in random networks Science 286:509-12 [PubMed]

Beggs JM, Plenz D (2003) Neuronal avalanches in neocortical circuits. J Neurosci 23:11167-77 [PubMed]

Blanchard P, Cessac B (2000) What can we learn about self-organized criticality from dynamical systems theory? J Stat Phys 98:357-404

Bollobas B (1985) Random Graphs

Börgers C, Kopell N (2003) Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural Comput 15:509-38 [Journal] [PubMed]

Burkitt AN, Clark GM (2001) Synchronization of the neural response to noisy periodic synaptic input. Neural Comput 13:2639-72 [Journal] [PubMed]

Cessac B, Blanchard P, Krüger T (2001) Lyapunov exponents and transport in the Zhang model of self-organized criticality. Phys Rev E Stat Nonlin Soft Matter Phys 64:016133 [Journal] [PubMed]

Chen D, Eu S, Guo A, Yang ZR (1995) Self-organized criticality in a cellular automaton model of pulse-coupled integrate-and-fire neurons J Phys A: Math Gen 28:5177-5182

Dauce E, Moynot O, Pinaud O, Samuelides M (2001) Mean-field theory and synchronization in random recurrent neural networks Neural Processing Letters 14:115-126

Dhar D (1990) Self-organized state of sand pile automaton models Phys Rev Lett 64:1613-1616

Dickman R (2000) Paths to selforganized criticality Brazilian J Physics 30:27-41

Dorogovtsev SN, Mendes JFF (2003) Evolution of networks

Edgar GA (1992) Measure, topology, and fractal geometry

Edgar GA, Golds J (1999) A fractal dimension estimate for a graph-directed iterated function system of non-similarities Indiana Univ Math J 48:429-447

Feng J, Brown D (1998) Fixed-point attractor analysis for a class of neurodynamics Neural Comput 10:189-213

Gerstner W, Kistler WM (2002) Spiking neuron models

Giacometti A, Diaz-Guilera A (1998) Dynamical properties of the Zhang model of self-organized criticality Phys Rev E 58:247-253

Goh KI, Lee DS, Kahng B, Kim D (2003) Sandpile on scale-free networks Phys Rev Lett 91:1487-1491

Golomb D, Hansel D (2000) The number of synaptic inputs and the synchrony of large, sparse neuronal networks. Neural Comput 12:1095-139 [PubMed]

Hergarten S (2002) Self-organized criticality in earth systems

Hertz J, Krogh A, Palmer RG (1991) Introduction to the Theory of Neural Computation.

Hopfield JJ, Brody CD (2001) What is a moment? Transient synchrony as a collective mechanism for spatiotemporal integration. Proc Natl Acad Sci U S A 98:1282-7 [Journal] [PubMed]

   Hopfield and Brody model (Hopfield, Brody 2000) [Model]
   Hopfield and Brody model (Hopfield, Brody 2000) (NEURON+python) [Model]

Hutchinson JE (1981) Fractals and self similarity Indiana Univ Math J 30:713-747

Jensen HJ (1998) Self-organized criticality

Kandel ER, Schwartz JH, Jessell TM (2000) Principles of neural science (4th ed), Kandel ER:Schwartz JH:Jessell TM, ed.

Lago-Fernandez LF, Corbacho FJ, Huerta R (2005) Connection topology dependence of synchronization of neural assemblies on class 1 and 2 excitability. Neural Netw 14:687-96

Lee HY, Lee HW, Kim D (1998) Origin of synchronized traffic flow on highways and its dynamic phase transition Phys Rev Lett 81:1130-1133

Lehnertz K, Andrzejak RG, Arnhold J, Widman G, Burr W, David P, Elger CE (2000) Possible clinical and research applications of nonlinear EEG analysis in humans Chaos in Brain?, Lehnertz K:Arnhold J:Grassberger P:Elger CE, ed. pp.134

Lubeck S, Rajewsky N, Wolf DE (2000) A deterministic sandpile automaton revisited Eur Phys J B 13:715-721

Markosová M, Markos P (1992) Analytical calculation of the attractor periods of deterministic sandpiles. Phys Rev A 46:3531-3534 [PubMed]

Newman ME, Strogatz SH, Watts DJ (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E Stat Nonlin Soft Matter Phys 64:026118 [Journal] [PubMed]

Nishikawa T, Motter AE, Lai YC, Hoppensteadt FC (2003) Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? Phys Rev Lett 91:014101 [Journal] [PubMed]

Pecora LM, Barahona M (2005) Synchronization of oscillators in complex networks Chaos Compl Lett 1:61-91

Perez CJ, Corral A, Diaz-guilera A (1996) On self-organized criticality and synchronization in lattice models of coupled dynamical systems J Mod Phys B 10:1-41

Trappenberg TP (2002) Fundamentals of computational neuroscience

Volk D (2000) Spontaneous synchronization in a discrete neural network model Chaos in brain?, Lehnertz K:Arnhold J:Grassberger P:Elger CE, ed. pp.234

Zhang YC (1989) Scaling theory of self-organized criticality. Phys Rev Lett 63:470-473 [Journal] [PubMed]

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