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Brown E, Moehlis J, Holmes P (2004) On the phase reduction and response dynamics of neural oscillator populations. Neural Comput 16:673-715 [PubMed]

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References and models that cite this paper

Aston-Jones G, Chen S, Zhu Y, Oshinsky ML (2001) A neural circuit for circadian regulation of arousal. Nat Neurosci 4:732-8 [Journal] [PubMed]
Aston-Jones G, Rajkowski J, Cohen J (2000) Locus coeruleus and regulation of behavioral flexibility and attention. Prog Brain Res 126:165-82 [Journal] [PubMed]
Aston-Jones G, Rajkowski J, Kubiak P, Alexinsky T (1994) Locus coeruleus neurons in monkey are selectively activated by attended cues in a vigilance task. J Neurosci 14:4467-80 [PubMed]
Bogacz R, Yeung N, Holroyd C (2002) Detection of phase resetting in the electroencephalogram: An evaluation of methods Soc Neurosci Abstr
Bressloff PC, Coombes S (2000) Dynamics of strongly-coupled spiking neurons. Neural Comput 12:91-129 [PubMed]
Brown E, Holmes P, Moehlis J (2003) Globally coupled oscillator networks Problems and perspectives in nonlinear science, A celebratory volume in honor of Lawrence Sirovich, Kaplan E:Marsden J:Sreenivasan K, ed. pp.183
Brown E, Moehlis J, Holmes P, Clayton E, Rajkowski J, Aston-Jones G (2004) The influence of spike rate and stimulus duration on noradrenergic neurons. J Comput Neurosci 17:13-29 [Journal] [PubMed]
Brunel N, Chance FS, Fourcaud N, Abbott LF (2001) Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 86:2186-9 [Journal] [PubMed]
Casti AR, Omurtag A, Sornborger A, Kaplan E, Knight B, Victor J, Sirovich L (2002) A population study of integrate-and-fire-or-burst neurons. Neural Comput 14:957-86 [Journal] [PubMed]
Coddington E, Levinson N (1955) Theory of Ordinary Differential Equations
Eckhorn R (1999) Neural mechanisms of scene segmentation: recordings from the visual cortex suggest basic circuits for linking field models. IEEE Trans Neural Netw 10:464-79 [Journal] [PubMed]
Ermentrout B (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comput 8:979-1001 [PubMed]
Ermentrout B, Kopell N (1984) Frequency plateaus in a chain of weakly coupled oscillators. Siam J Math Anal 15:215-237
Ermentrout GB (1981) Phase-locking of weakly coupled oscillators J Math Biol 12:327-342
Ermentrout GB (2002) Simulating, Analyzing, and Animating Dynamical System: A Guide to XPPAUT for Researchers and Students Society for Industrial and Applied Mathematics (SIAM)
Ermentrout GB, Kopell N (1990) Oscillator death in systems of coupled neural oscillators SIAM J App Math 51:125-146
Ermentrout GB, Kopell N (1991) Multiple pulse interactions and averaging in systems of coupled neural oscillators. J Math Biol 29:195-217
Evans L (1998) Partial Differential Equations
Fenichel N (1971) Persistence and smoothness of invariant manifolds for flows Ind Univ Math J 21:193-225
Fetz EE, Gustafsson B (1983) Relation between shapes of post-synaptic potentials and changes in firing probability of cat motoneurones. J Physiol 341:387-410 [PubMed]
Fourcaud N, Brunel N (2002) Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput 14:2057-110 [Journal] [PubMed]
Gerstner W (2000) Population dynamics of spiking neurons: fast transients, asynchronous states, and locking. Neural Comput 12:43-89 [PubMed]
Gerstner W, Kistler WM (2002) Spiking neuron models
Gerstner W, van Hemmen JL, Cowan JD (1996) What matters in neuronal locking? Neural Comput 8:1653-76 [PubMed]
Glass L, Mackey MC (1988) From Clocks To Chaos: The Rhythms Of Life
Gray CM (1999) The temporal correlation hypothesis of visual feature integration: still alive and well. Neuron 24:31-47, 111-25 [PubMed]
Guckenheimer J (1975) Isochrons and phaseless sets. J Math Biol 1:259-273 [Journal] [PubMed]
Guckenheimer J, Holmes P (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2nd edition.
Hansel D, Mato G, Meunier C (1993) Phase dynamics for weakly coupled Hodgkin-Huxley neurons. Europhys Lett 23:367-372
Hansel D, Mato G, Meunier C (1995) Synchrony in excitatory neural networks. Neural Comput 7:307-37 [PubMed]
Herrmann A, Gerstner W (2001) Noise and the PSTH response to current transients: I. General theory and application to the integrate-and-fire neuron. J Comput Neurosci 11:135-51 [PubMed]
Hoppensteadt FC, Izhikevich EM (1997) Weakly Connected Neural Networks :90
Izhikevich EM (2000) Phase equations for relaxation oscillations Siam J Appl Mat 60:1789-1804
Izhikevich EM (2000) Neural excitability, spiking and bursting Int J Bifurcat Chaos Appl Sci Eng 10:1171-1266
Keener J, Sneyd J (1998) Mathematical Physiology Interdisciplinary Applied Mathematics
Kim S, Lee S (2000) Phase dynamics in the biological neural networks Physica D 288:380-396
Kuramoto Y (1984) Chemical oscillations, waves, and turbulence
Kuramoto Y (1997) Phase- and center-manifold reductions for large populations of coupled oscillators with application to non-locally coupled systems Int J Bif Chaos 7:789-805
Kuznetsov Y (1998) Elements of applied bifurcation theory (2nd ed.)
Lewis TJ, Rinzel J (2003) Dynamics of spiking neurons connected by both inhibitory and electrical coupling. J Comput Neurosci 14:283-309 [PubMed]
Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268:1503-6 [PubMed]
Makeig S, Westerfield M, Jung TP, Enghoff S, Townsend J, Courchesne E, Sejnowski TJ (2002) Dynamic brain sources of visual evoked responses. Science 295:690-4 [Journal] [PubMed]
Malkin IG (1949) Methods of Poincare and Lyapunov in the theory of non-linear oscillations
Matell MS, Meck WH (2000) Neuropsychological mechanisms of interval timing behavior. Bioessays 22:94-103 [Journal] [PubMed]
Moore RY, Bloom FE (1979) Central catecholamine neuron systems: anatomy and physiology of the norepinephrine and epinephrine systems. Annu Rev Neurosci 2:113-68 [Journal] [PubMed]
Murray J (2002) Mathematical biology I: An introduction (3rd Ed)
Nykamp DQ, Tranchina D (2000) A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. J Comput Neurosci 8:19-50 [PubMed]
Omurtag A, Knight BW, Sirovich L (2000) On the simulation of large populations of neurons. J Comput Neurosci 8:51-63 [PubMed]
Rinzel J, Ermentrout B (1998) Analysis of neural excitability and oscillations. Methods In Neuronal Modeling 2nd Edition, Segev I, Koch C, ed. pp.251
Rinzel J, Miller R (1980) Numerical calculation of stable and unstable periodic solutions to the Hodgkin-Huxley equations Math Biosci 49:27-59
Ritt J (2003) A Probabilistic Analysis of Forced Oscillators, with Application to Neuronal Response Reliability PhD Thesis
Rose RM, Hindmarsh JL (1989) The assembly of ionic currents in a thalamic neuron. I. The three-dimensional model. Proc R Soc Lond B Biol Sci 237:267-88 [Journal] [PubMed]
Servan-Schreiber D, Printz H, Cohen JD (1990) A network model of catecholamine effects: gain, signal-to-noise ratio, and behavior. Science 249:892-5 [PubMed]
STEIN RB (1965) A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY. Biophys J 5:173-94 [PubMed]
Strogatz S (2000) From Kuramoto to Crawford: Explaining the onset of synchronization in populations of globally coupled oscillators Physica D 143:1-20
Tass P (1999) Phase Resetting in Medicine and Biology
Usher M, Cohen JD, Servan-Schreiber D, Rajkowski J, Aston-Jones G (1999) The role of locus coeruleus in the regulation of cognitive performance. Science 283:549-54 [PubMed]
Van Vreeswijk C, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J Comput Neurosci 1:313-21 [PubMed]
Whitham GB (1974) Linear and Nonlinear Waves
Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12:1-24 [Journal] [PubMed]
   Excitatory and inhibitory interactions in populations of model neurons (Wilson and Cowan 1972) [Model]
Winfree A (1974) Patterns of phase compromise in biological cycles J Math Biol 1:73-95
Winfree A (2001) The Geometry of Biological Time (2nd ed)
Beverlin B, Kakalios J, Nykamp D, Netoff TI (2012) Dynamical changes in neurons during seizures determine tonic to clonic shift. J Comput Neurosci 33:41-51 [Journal] [PubMed]
   Epileptic seizure model with Morris-Lecar neurons (Beverlin and Netoff 2011) [Model]
Bogaard A, Parent J, Zochowski M, Booth V (2009) Interaction of cellular and network mechanisms in spatiotemporal pattern formation in neuronal networks. J Neurosci 29:1677-87 [Journal] [PubMed]
   Small world networks of Type I and Type II Excitable Neurons (Bogaard et al. 2009) [Model]
Brown E, Moehlis J, Holmes P, Clayton E, Rajkowski J, Aston-Jones G (2004) The influence of spike rate and stimulus duration on noradrenergic neurons. J Comput Neurosci 17:13-29 [Journal] [PubMed]
Dumont G, Ermentrout GB, Gutkin B (2017) Macroscopic phase-resetting curves for spiking neural networks. Phys Rev E 96:042311 [Journal] [PubMed]
Ermentrout GB, Terman DH (2010) Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics, Antman SS:Marsden JE:Sirovich L:Wiggins, ed. pp.1 [Journal]
   Mathematical Foundations of Neuroscience (Ermentrout and Terman 2010) [Model]
Goldberg JA, Deister CA, Wilson CJ (2007) Response properties and synchronization of rhythmically firing dendritic neurons. J Neurophysiol 97:208-19 [Journal] [PubMed]
   Role of active dendrites in rhythmically-firing neurons (Goldberg et al 2006) [Model]
Govaerts W, Sautois B (2006) Computation of the phase response curve: a direct numerical approach. Neural Comput 18:817-47 [Journal] [PubMed]
Kilinc D, Demir A (2017) Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques. IEEE Trans Biomed Circuits Syst 11:958-974 [Journal] [PubMed]
   A neuronal circuit simulator for non Monte Carlo analysis of neuronal noise (Kilinc & Demir 2018) [Model]
Ly C, Tranchina D (2007) Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling. Neural Comput 19:2032-92 [Journal] [PubMed]
Oh M, Matveev V (2009) Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons. J Comput Neurosci 26:303-20 [Journal] [PubMed]
   Loss of phase-locking in non-weakly coupled inhib. networks of type-I neurons (Oh and Matveev 2009) [Model]
Oprisan SA (2017) Predicting the Existence and Stability of Phase-Locked Mode in Neural Networks Using Generalized Phase-Resetting Curve. Neural Comput 29:2030-2054 [Journal] [PubMed]
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