Citation Relationships

Legends: Link to a Model Reference cited by multiple papers


Brette R (2004) Dynamics of one-dimensional spiking neuron models. J Math Biol 48:38-56 [PubMed]

   Phase locking in leaky integrate-and-fire model (Brette 2004)

References and models cited by this paper

References and models that cite this paper

Alstrom P, Christiansen B, Levinsen MT (1988) Nonchaotic transition from quasiperiodicity to complete phase locking. Phys Rev Lett 61:1679-1682 [Journal] [PubMed]
Artun OB, Shouval HZ, Cooper LN (1998) The effect of dynamic synapses on spatiotemporal receptive fields in visual cortex. Proc Natl Acad Sci U S A 95:11999-2003 [PubMed]
Ascoli C, Barbi M, Chillemi S, Petracchi D (1977) Phase-locked responses in the Limulus lateral eye. Theoretical and experimental investigation. Biophys J 19:219-40 [Journal] [PubMed]
Brette R (2003) Rotation numbers of discontinuous orientation-preserving circle maps Set-Valued Analysis 11(4):359-371
Brette R, Guigon E (2003) Reliability of spike timing is a general property of spiking model neurons. Neural Comput 15:279-308 [Journal] [PubMed]
   Reliability of spike timing is a general property of spiking model neurons (Brette & Guigon 2003) [Model]
Coombes S (1999) Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems Phys. Lett. A 255(1-2):49-57
Cornfeld I, Fomin S, Sinai Y (1981) Ergodic theory Grundlehren der mathematischen Wissenschaften
De_melo W, Van_strien S (1993) One-dimensional dynamics
Denjoy A (1932) Sur les courbes definies par les equations differentielles a la surface du tore J Math Pures Appl 9:333-375
Ermentrout B (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comput 8:979-1001 [PubMed]
Ermentrout GB, Kopell N (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. Siam J Appl Math 46:233-253
Glass L, Belair J (1986) Continuation of Arnold tongues in mathematical models of periodically forced biological oscillators Lecture Notes in Biomathematics 66:232-243
Glass L, Perez R (1982) Fine structure of phase locking Phys Rev Lett 48:1772-1775
Guttman R, Feldman L, Jakobsson E (1980) Frequency entrainment of squid axon membrane. J Membr Biol 56:9-18 [PubMed]
Herman M (1977) Mesure de Lebesgue et nombre de rotation Lecture Notes in Math 597:271-293
Jensen M, Bak P, Bohr T (1983) Complete devil's staircase, fractal dimension and universality of mode-locking structure in the circle map Phys Rev Lett 50:1637-1639
Keener J, Hoppensteadt F, Rinzel J (1981) Integrate-and-fire models of nerve membrane response to oscillatory input. Siam J Appl Math 41:503-517
Keener JP (1980) Chaotic behavior in piecewise continuous difference equations Trans Of The AMS 261:589-604
Knight BW (1972) Dynamics of encoding in a population of neurons. J Gen Physiol 59:734-66 [PubMed]
Köppl C (1997) Phase locking to high frequencies in the auditory nerve and cochlear nucleus magnocellularis of the barn owl, Tyto alba. J Neurosci 17:3312-21 [PubMed]
Kwapisz J (2000) Poincare rotation number for maps of the real line with almost periodic displacement Nonlinearity 13:1841-1854
Lapicque L (1907) Recherches quantitatives sur lexcitation electrique des nerfs traitee comme une polarisation J Physiol Pathol Gen 9:620-635 [Journal]
Latham PE, Richmond BJ, Nelson PG, Nirenberg S (2000) Intrinsic dynamics in neuronal networks. I. Theory. J Neurophysiol 83:808-27 [Journal] [PubMed]
Poincare H (1885) Sur les courbes definies par les equations differentielles J Math Pures App I
Rescigno A, Stein RB, Purple RL, Poppele RE (1970) A neuronal model for the discharge patterns produced by cyclic inputs. Bull Math Biophys 32:337-53 [PubMed]
Rhodes F, Thompson C (1986) Rotation numbers for monotone functions on the circle J London Math Soc 2:360-368
Rhodes F, Thompson C (1991) Topologies and rotation numbers for families of monotone functions on the circle J London Math Soc 2:156-170
Somers DC, Nelson SB, Sur M (1995) An emergent model of orientation selectivity in cat visual cortical simple cells. J Neurosci 15:5448-65 [PubMed]
Song S, Abbott LF (2001) Cortical development and remapping through spike timing-dependent plasticity. Neuron 32:339-50 [PubMed]
Song S, Miller KD, Abbott LF (2000) Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nat Neurosci 3:919-26 [Journal] [PubMed]
Swiatek G (1988) Rational rotation numbers for maps of the circle Commun Math Phys 119:109-128
Tass P, Rosenblum M, Weule J, Kurths J, Pikovsky A, Volkmann J, Schnitzler A, Freund H (1998) Detection of n:m phase locking from noisy data: Application to magnetoencephalography Phys Rev Lett 81:3291-3294
Tiesinga PHE (2002) Phys Rev E 65:041913
Troyer TW, Miller KD (1997) Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Comput 9:971-83 [PubMed]
Veerman JJP (1989) Irrational rotation numbers Nonlinearity 2:419-428
Brette R (2012) Computing with neural synchrony. PLoS Comput Biol 8:e1002561 [Journal] [PubMed]
   Computing with neural synchrony (Brette 2012) [Model]
Touboul J, Brette R (2008) Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Biol Cybern 99:319-34 [Journal] [PubMed]
   Brette-Gerstner model (Touboul and Brette 2008) [Model]
(38 refs)