Dynamical Systems in Neuroscience:
Dynamical Systems in Neuroscience: Dynamical Systems in Neuroscience:
454 ReferencesTuckwell H.C. (1988) Introduction to Theoretical Neurobiology. Cambridge, UK, CambridgeUniversity Press.Uhlenbeck G.E. and Ornstein L.S. (1930) On the theory of the Brownian motion. Phys. Rev.36:823–841.van Vreeswijk C., Abbott L.F., Ermentrout G.B. (1994) When inhibition not excitation synchronizesneural firing. Journal of Computational Neuroscience, 1:313–321van Vreeswijk C. and Hansel D. (2001) Patterns of Synchrony in Neural Networks with SpikeAdaptation. Neural Comp. 13:959–992van Vreeswijk C. (2000) Analysis of the Asynchronous State in Networks of Strongly CoupledOscillators. Physical Review Letters, 84, 5110–5113.de Vries G. (1998) Multiple Bifurcations in a Polynomial Model of Bursting Oscillations. Journalof Nonlinear Science, 8:281–316.Wang X.-J. (1999) Fast burst firing and short-term synaptic plasticity: a model of neocorticalchattering neurons. Neuroscience 89:347-362.Wang X.-J. and Rinzel J. (1992) Alternating and synchronous rhythms in reciprocally inhibitorymodel neurons. Neural Computation. 4:84–97.Wechselberger M. (2005) Existence and Bifurcation of Canards in R 3 in the Case of a FoldedNode. SIAM J. Appl. Dynamical Systems, 4:101–139.Wessel R., Kristan W.B., and Kleinfeld D. (1999) Supralinear Summation of Synaptic Inputs byan Invertebrate Neuron: Dendritic Gain Is Mediated by an “Inward Rectifier” K + Current.The Journal of Neuroscience, 19:5875–5888.White J.A., Rubinstein J. T., and Kay A. R. (2000) Channel noise in neurons.Neuroscience, 23:131–137.Trends inWilliams J.T., North R.A., and Tokimasa T. (1988) Inward Rectification of Resting and Opiate-Activated Potassium Currents in Rat Locus Coeruleus Neurons. The Journal of Neuroscience,8:4299–4306Williams S.R. and Stuart G.J. (2003) Role of dendritic synapse location in the control of actionpotential. TINS, 26:147–154.Willms A.R., Baro D.J., Harris-Warrick R.M., and Guckenheimer J. (1999) An Improved ParameterEstimation Method for Hodgkin-Huxley Models, Journal of Computational Neuroscience,6:145–168.Wilson C.J. (1993) The generation of natural firing patterns in neostriatal neurons. In Progressin Brain Research. (Arbuthnott G., Emson P.C. eds),277–297. Amsterdam. ElsevierWilson C. J. and Groves P. M. (1981) Spontaneous firing patterns of identified spiny neuronsin the rat neostriatum. Brain Research, 220:67–80Wilson H.R. and Cowan J.D. (1972) Excitatory and inhibitory interaction in localized populationsof model neurons. Biophys J 12:1–24.Wilson H.R. and Cowan J.D. (1973) A Mathematical theory of the functional dynamics ofcortical and thalamic nervous tissue. Kybernetik 13:55–80.Wilson H.R. (1999) Spikes, Decisions, and Actions: The dynamical foundations of neuroscience.
References 455Oxford University Press.Winfree A. (1967) Biological Rhythms and the Behavior of Populations of Coupled Oscillators.Journal of Theoretical Biology, 16:15–42.Winfree A. (1974) Patterns of Phase Compromise in Biological Cycles. Journal of Math. Biology1:73–95.Winfree A. (2001) The Geometry of Biological Time. Springer-Verlag, New York, second edition.Wolfram S. (2002) A New Kind of Science. Wolfram Media.Wu N., Hsiao C.-F., Chandler S. (2001) Membrane resonance and subthreshold membrane oscillationsin mesencephalic V neurons: participants in burst generation. J. Neurosci 21:3729–3739.Young G. (1937) Psychometrika, 2:103.Yuan A., Dourado M., Butler A., Walton N., Wei A., Salkoff L. (2000) SLO-2, a K + channelwith an unusual Cl − dependence. Nature Neurscience, 3:771–779.Yuan A., Santi C.M., Wei A., Wang Z.W., Pollak K., Nonet M., Kaczmarek L., Crowder C.M.,Salkoff L. (2003) The sodium-activated potassium channel is encoded by a member of the Slogene family. Neuron. 37:765–773.Yue C. and Yaari Y. (2004) KCNQ/M Channels Control Spike Afterdepolarization and BurstGeneration in Hippocampal Neurons. J. Neuroscience, 24:4614–4624.Zhan, X. J., Cox C. L., Rinzel J., and Sherman S. M. (1999) Current clamp and modelingstudies of low-threshold calcium spikes in cells of the cat’s lateral geniculate nucleus. J.Neurophysiol. 81:2360–2373.
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- Page 452 and 453: 442 Referencesterneurons mediated b
- Page 454 and 455: 444 ReferencesDickson C.T., Magistr
- Page 456 and 457: 446 ReferencesGuckenheimer J. (1975
- Page 458 and 459: 448 Referencestional Journal of Bif
- Page 460 and 461: 450 ReferencesMarkram H, Toledo-Rod
- Page 462 and 463: 452 ReferencesRosenblum M.G. and Pi
- Page 466 and 467: 456 References9
- Page 468 and 469: 458 Synchronization (see www.izhike
- Page 470 and 471: 460 Synchronization (see www.izhike
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- Page 512 and 513: 502 Synchronization (see www.izhike
454 ReferencesTuckwell H.C. (1988) Introduction to Theoretical Neurobiology. Cambridge, UK, CambridgeUniversity Press.Uhlenbeck G.E. and Ornste<strong>in</strong> L.S. (1930) On the theory of the Brownian motion. Phys. Rev.36:823–841.van Vreeswijk C., Abbott L.F., Ermentrout G.B. (1994) When <strong>in</strong>hibition not excitation synchronizesneural fir<strong>in</strong>g. Journal of Computational <strong>Neuroscience</strong>, 1:313–321van Vreeswijk C. and Hansel D. (2001) Patterns of Synchrony <strong>in</strong> Neural Networks with SpikeAdaptation. Neural Comp. 13:959–992van Vreeswijk C. (2000) Analysis of the Asynchronous State <strong>in</strong> Networks of Strongly CoupledOscillators. Physical Review Letters, 84, 5110–5113.de Vries G. (1998) Multiple Bifurcations <strong>in</strong> a Polynomial Model of Burst<strong>in</strong>g Oscillations. Journalof Nonl<strong>in</strong>ear Science, 8:281–316.Wang X.-J. (1999) Fast burst fir<strong>in</strong>g and short-term synaptic plasticity: a model of neocorticalchatter<strong>in</strong>g neurons. <strong>Neuroscience</strong> 89:347-362.Wang X.-J. and R<strong>in</strong>zel J. (1992) Alternat<strong>in</strong>g and synchronous rhythms <strong>in</strong> reciprocally <strong>in</strong>hibitorymodel neurons. Neural Computation. 4:84–97.Wechselberger M. (2005) Existence and Bifurcation of Canards <strong>in</strong> R 3 <strong>in</strong> the Case of a FoldedNode. SIAM J. Appl. <strong>Dynamical</strong> <strong>Systems</strong>, 4:101–139.Wessel R., Kristan W.B., and Kle<strong>in</strong>feld D. (1999) Supral<strong>in</strong>ear Summation of Synaptic Inputs byan Invertebrate Neuron: Dendritic Ga<strong>in</strong> Is Mediated by an “Inward Rectifier” K + Current.The Journal of <strong>Neuroscience</strong>, 19:5875–5888.White J.A., Rub<strong>in</strong>ste<strong>in</strong> J. T., and Kay A. R. (2000) Channel noise <strong>in</strong> neurons.<strong>Neuroscience</strong>, 23:131–137.Trends <strong>in</strong>Williams J.T., North R.A., and Tokimasa T. (1988) Inward Rectification of Rest<strong>in</strong>g and Opiate-Activated Potassium Currents <strong>in</strong> Rat Locus Coeruleus Neurons. The Journal of <strong>Neuroscience</strong>,8:4299–4306Williams S.R. and Stuart G.J. (2003) Role of dendritic synapse location <strong>in</strong> the control of actionpotential. TINS, 26:147–154.Willms A.R., Baro D.J., Harris-Warrick R.M., and Guckenheimer J. (1999) An Improved ParameterEstimation Method for Hodgk<strong>in</strong>-Huxley Models, Journal of Computational <strong>Neuroscience</strong>,6:145–168.Wilson C.J. (1993) The generation of natural fir<strong>in</strong>g patterns <strong>in</strong> neostriatal neurons. In Progress<strong>in</strong> Bra<strong>in</strong> Research. (Arbuthnott G., Emson P.C. eds),277–297. Amsterdam. ElsevierWilson C. J. and Groves P. M. (1981) Spontaneous fir<strong>in</strong>g patterns of identified sp<strong>in</strong>y neurons<strong>in</strong> the rat neostriatum. Bra<strong>in</strong> Research, 220:67–80Wilson H.R. and Cowan J.D. (1972) Excitatory and <strong>in</strong>hibitory <strong>in</strong>teraction <strong>in</strong> localized populationsof model neurons. Biophys J 12:1–24.Wilson H.R. and Cowan J.D. (1973) A Mathematical theory of the functional dynamics ofcortical and thalamic nervous tissue. Kybernetik 13:55–80.Wilson H.R. (1999) Spikes, Decisions, and Actions: The dynamical foundations of neuroscience.