References and models cited by this paper

References and models that cite this paper

Acker CD, Kopell N, White JA (2003) Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics. J Comput Neurosci 15:71-90 [PubMed]

Alonso A, García-Austt E (1987) Neuronal sources of theta rhythm in the entorhinal cortex of the rat. I. Laminar distribution of theta field potentials. Exp Brain Res 67:493-501 [PubMed]

Alonso A, Klink R (1993) Differential electroresponsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II. J Neurophysiol 70:128-43 [Journal] [PubMed]

Alonso A, Llinás RR (1989) Subthreshold Na+-dependent theta-like rhythmicity in stellate cells of entorhinal cortex layer II. Nature 342:175-7 [Journal] [PubMed]

Baer SM, Erneux T, Rinzel J (1989) The slow passage through Hopf bifurcation: delay, memory ecects, and resonance. J Appl Math 49:55-71

Benoit E, Callot JL, Dienner F (1980) Chasse au Canard

Brons M, Krupa M, Wechselberger M (2006) Mixed mode oscillations due to the generalized canard phenomenon Fields Institute Communications 49:39-63

Burden RL, Faires JD (1980) Numerical Analysis

Buzsáki G (1989) Two-stage model of memory trace formation: a role for "noisy" brain states. Neuroscience 31:551-70 [PubMed]

Buzsáki G, Draguhn A (2004) Neuronal oscillations in cortical networks. Science 304:1926-9 [Journal] [PubMed]

Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys J 71:3013-21 [Journal] [PubMed]

Clewley R, Rotstein HG, Kopell N (2005) A Computational Tool for the Reduction of Nonlinear ODE Systems Possessing Multiple Scales Multiscale modeling & simulation 4(3):732-759 [Journal]

Dayan P, Abbott L (2001) Neural encoding: Firing rates and spike statistics Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems

Destexhe A, Mainen ZF, Sejnowski TJ (1994) Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J Comput Neurosci 1:195-230 [PubMed]

Dickson CT, Magistretti J, Shalinsky M, Hamam B, Alonso A (2000) Oscillatory activity in entorhinal neurons and circuits. Mechanisms and function. Ann N Y Acad Sci 911:127-50 [PubMed]

Dickson CT, Magistretti J, Shalinsky MH, Fransén E, Hasselmo ME, Alonso A (2000) Properties and role of I(h) in the pacing of subthreshold oscillations in entorhinal cortex layer II neurons. J Neurophysiol 83:2562-79 [Journal] [PubMed]

Drover J, Rubin J, Su J, Ermentrout B (2005) Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies SIAM J Appl Math 65:65-92

Dumortier F, Roussarie R (1996) Canard cycles and center manifolds Mem Am Math Soc 121:577

Eckhaus W (1983) Relaxation oscillations including a standard chase on french ducks Lecture Notes in Mathematics 985:449-497

Erchova I, Kreck G, Heinemann U, Herz AV (2004) Dynamics of rat entorhinal cortex layer II and III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold. J Physiol 560:89-110 [Journal] [PubMed]

Fenichel N (1971) Persistence and smoothness of invariant manifolds for flows Ind Univ Math J 21:193-225

Fransén E, Alonso AA, Dickson CT, Magistretti J, Hasselmo ME (2004) Ionic mechanisms in the generation of subthreshold oscillations and action potential clustering in entorhinal layer II stellate neurons. Hippocampus 14:368-84 [Journal] [PubMed]

Fransen E, Dickson C, Magistretti J, Alonso A, Hasselmo M (1998) Modeling the Generation of Subthreshold Membrane Potential Oscillations of Entorhinal Cortex Layer II Soc Neurosci Abstr 24:2036

Fransen E, Wallenstein GV, Alonso AA, Dickson CT, Hasselmo ME (1999) A biophysical simulation of intrinsic and network properties of entorhinal cortex Neurocomputing 26:375-380

Gillies MJ, Traub RD, LeBeau FE, Davies CH, Gloveli T, Buhl EH, Whittington MA (2002) A model of atropine-resistant theta oscillations in rat hippocampal area CA1. J Physiol 543:779-93 [PubMed]

Hutcheon B, Miura RM, Puil E (1996) Subthreshold membrane resonance in neocortical neurons. J Neurophysiol 76:683-97 [Journal] [PubMed]

Hutcheon B, Yarom Y (2000) Resonance, oscillation and the intrinsic frequency preferences of neurons. Trends Neurosci 23:216-22 [PubMed]

Izhikevich EM (2003) Resonate-and-fire neurons. Neural Netw 14:883-94

Izhikevich EM (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [Journal]

Jalics J, Kispersky T, Dickson C, Kopell N (2004) Neuronal ensembles and modules: Modeling dynamics in medial entorhinal cortex Soc Neurosci Abstr 517.1

Jalics J, Rotstein HG, Kopell N (2005) Unpublished data

Kahana MJ, Sekuler R, Caplan JB, Kirschen M, Madsen JR (1999) Human theta oscillations exhibit task dependence during virtual maze navigation. Nature 399:781-4 [Journal] [PubMed]

Klink R, Alonso A (1993) Ionic mechanisms for the subthreshold oscillations and differential electroresponsiveness of medial entorhinal cortex layer II neurons. J Neurophysiol 70:144-57 [Journal] [PubMed]

Klink R, Alonso A (1997) Ionic mechanisms of muscarinic depolarization in entorhinal cortex layer II neurons. J Neurophysiol 77:1829-43 [Journal] [PubMed]

Koch C (1999) Biophysics Of Computation: Information Processing in Single Neurons

Kopell N, LeMasson G (1994) Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture. Proc Natl Acad Sci U S A 91:10586-90 [PubMed]

Krupa M, Szmolyan P (2001) Relaxation oscillation and canard explosion J Diff Eq 174:312-368

Llinás R, Yarom Y (1981) Electrophysiology of mammalian inferior olivary neurones in vitro. Different types of voltage-dependent ionic conductances. J Physiol 315:549-67 [PubMed]

Llinás R, Yarom Y (1986) Oscillatory properties of guinea-pig inferior olivary neurones and their pharmacological modulation: an in vitro study. J Physiol 376:163-82 [PubMed]

Magistretti J, Alonso A (1999) Biophysical properties and slow voltage-dependent inactivation of a sustained sodium current in entorhinal cortex layer-II principal neurons: a whole-cell and single-channel study. J Gen Physiol 114:491-509 [PubMed]

Magistretti J, Ragsdale DS, Alonso A (1999) High conductance sustained single-channel activity responsible for the low-threshold persistent Na(+) current in entorhinal cortex neurons. J Neurosci 19:7334-41 [PubMed]

Makarov VA, Nekorkin VI, Velarde MG (2001) Spiking behavior in a noise-driven system combining oscillatory and excitatory properties. Phys Rev Lett 86:3431-4

Neishtadt AI (1987) On delayed stability loss under dynamical bifurcations I. J Diff Eqn 23:1385-1390

Neishtadt AI (1988) Persistence of stability loss for dynamical bifurcations II Diff Eqn 24:171-176

Netoff T, Banks M, White J (2003) Bridging single cell and network dynamics Soc Neurosci Abstr 32:171.7

Netoff TI, Pervouchine D, Kopell N, White JA (2004) Oscillation frequency switches in model and hybrid networks of the hippocampus Soc Neurosci Abstr :741

Pervouchine DD, Netoff TI, Rotstein HG, White JA, Cunningham MO, Whittington MA, Kopell NJ (2006) Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus. Neural Comput 18:2617-50 [Journal] [PubMed]

Richardson MJ, Brunel N, Hakim V (2003) From subthreshold to firing-rate resonance. J Neurophysiol 89:2538-54 [Journal] [PubMed]

Rinzel J (1985) Excitation dynamics: insights from simplified membrane models. Fed Proc 44:2944-6 [PubMed]

Rotstein HG, Clewley R, Wechselberger M, Kopell N (2005) Reduction of dimensions and dynamics of a medial entorhinal cortex layer II stellate cell model In Preparation

Rotstein HG, Pervouchine DD, Acker CD, Gillies MJ, White JA, Buhl EH, Whittington MA, Kopell N (2005) Slow and fast inhibition and an H-current interact to create a theta rhythm in a model of CA1 interneuron network. J Neurophysiol 94:1509-18 [Journal] [PubMed]

Schreiber S, Erchova I, Heinemann U, Herz AV (2004) Subthreshold resonance explains the frequency-dependent integration of periodic as well as random stimuli in the entorhinal cortex. J Neurophysiol 92:408-15 [Journal] [PubMed]

Shalinsky MH, Magistretti J, Ma L, Alonso AA (2002) Muscarinic activation of a cation current and associated current noise in entorhinal-cortex layer-II neurons. J Neurophysiol 88:1197-211 [Journal] [PubMed]

Spain WJ, Schwindt PC, Crill WE (1987) Anomalous rectification in neurons from cat sensorimotor cortex in vitro. J Neurophysiol 57:1555-76 [Journal] [PubMed]

Szmolyan P, Wechselberger M (2001) Canards in 3 J Diff Eqn 177:419-453

Wechselberger M (2005) Existence and bifurcation of canards in 3 in the case of a folded node SIAM J Appl Dynam Sys 4:101-139

White JA, Budde T, Kay AR (1995) A bifurcation analysis of neuronal subthreshold oscillations. Biophys J 69:1203-17 [Journal] [PubMed]

White JA, Klink R, Alonso A, Kay AR (1998) Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J Neurophysiol 80:262-9 [Journal] [PubMed]

White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:131-7 [PubMed]

Winson J (1978) Loss of hippocampal theta rhythm results in spatial memory deficit in the rat. Science 201:160-3 [PubMed]

Hummos A, Nair SS (2017) An integrative model of the intrinsic hippocampal theta rhythm. PLoS One 12:e0182648 [Journal] [PubMed]

Joos B, Barlow BM, Morris CE (2018) Calculating the Consequences of Left-Shifted Nav Channel Activity in Sick Excitable Cells. Handb Exp Pharmacol 246:401-422 [Journal] [PubMed]

Kopell N, Borgers C, Pervouchine D, Malerba P, Tort ABL (2010) Gamma and theta rhythms in biophysical models of hippocampal circuits Hippocampal Microcircuits: A Computational Modeller`s Resource Book. Ch. 15., Cutsuridis V, Graham BF, Cobb S, Vida I, ed. [Journal]

Vich C, Berg RW, Guillamon A, Ditlevsen S (2017) Estimation of Synaptic Conductances in Presence of Nonlinear Effects Caused by Subthreshold Ionic Currents. Front Comput Neurosci 11:69 [Journal] [PubMed]

Vich C, Guillamon A (2015) Dissecting estimation of conductances in subthreshold regimes. J Comput Neurosci 39:271-87 [Journal] [PubMed]