-
1
-
-
80051966427
-
The CaV3.3 calcium channel is the major sleep spindle pacemaker in thalamus
-
S. Astori, R. D. Wimmer, H. M Prosser, C. Corti, M. Corsi, N. Liaudet, A. Volterra, P. Franken, J. P. Adelman, and A. Lüthi, The CaV3.3 calcium channel is the major sleep spindle pacemaker in thalamus, Proc. Natl. Acad. Sci. USA, 108 (2011), pp. 13823-13828.
-
(2011)
Proc. Natl. Acad. Sci. USA
, vol.108
, pp. 13823-13828
-
-
Astori, S.1
Wimmer, R.D.2
Prosser, H.M.3
Corti, C.4
Corsi, M.5
Liaudet, N.6
Volterra, A.7
Franken, P.8
Adelman, J.P.9
Lüthi, A.10
-
2
-
-
0029303855
-
Topological and phenomenological classification of bursting oscillations
-
R. Bertram, M. J. Butte, T. Kiemel, and A. Sherman, Topological and phenomenological classification of bursting oscillations, Bull. Math. Biol., 57 (1995), pp. 413-439.
-
(1995)
Bull. Math. Biol.
, vol.57
, pp. 413-439
-
-
Bertram, R.1
Butte, M.J.2
Kiemel, T.3
Sherman, A.4
-
3
-
-
0033555825
-
Subthalamic nucleus neurons switch from single-spike activity to burst-firing mode
-
C Beurrier, P Congar, B Bioulac, and C Hammond, Subthalamic nucleus neurons switch from single-spike activity to burst-firing mode, J. Neurosci., 19 (1999), pp. 599-609.
-
(1999)
J. Neurosci.
, vol.19
, pp. 599-609
-
-
Beurrier, C.1
Congar, P.2
Bioulac, B.3
Hammond, C.4
-
4
-
-
0000184573
-
Homoclinic bifurcation at resonant eigenvalues
-
S.-N. Chow, B. Deng, and B. Fiedler, Homoclinic bifurcation at resonant eigenvalues, J. Dynam. Differential Equations, 2 (1990), pp. 177-244.
-
(1990)
J. Dynam. Differential Equations
, vol.2
, pp. 177-244
-
-
Chow, S.-N.1
Deng, B.2
Fiedler, B.3
-
5
-
-
0004005623
-
-
Cambridge University Press, Cambridge, UK
-
S.-N. Chow, C. Li, and D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge University Press, Cambridge, UK, 1994.
-
(1994)
Normal Forms and Bifurcation of Planar Vector Fields
-
-
Chow, S.-N.1
Li, C.2
Wang, D.3
-
6
-
-
84864702572
-
A novel phase portrait for neuronal excitability
-
G. Drion, A. Franci, V. Seutin, and R. Sepulchre, A novel phase portrait for neuronal excitability, PLoS ONE, 7 (2012), e41806.
-
(2012)
PLoS ONE
, vol.7
, pp. e41806
-
-
Drion, G.1
Franci, A.2
Seutin, V.3
Sepulchre, R.4
-
7
-
-
34250627892
-
Geometric singular perturbation theory for ordinary differential equations
-
N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations, 31 (1979), pp. 53-98.
-
(1979)
J. Differential Equations
, vol.31
, pp. 53-98
-
-
Fenichel, N.1
-
8
-
-
53349102813
-
Impulses and physiological states in theoretical models of nerve membrane
-
R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J., 1 (1961), pp. 445-466.
-
(1961)
Biophys. J.
, vol.1
, pp. 445-466
-
-
Fitzhugh, R.1
-
9
-
-
84871373684
-
An organizing center in a planar model of neuronal excitability
-
A. Franci, G. Drion, and R. Sepulchre, An organizing center in a planar model of neuronal excitability, SIAM J. Appl. Dyn. Syst., 11 (2012), pp. 1698-1722.
-
(2012)
SIAM SIAM J. Appl. Dyn. Syst.
, vol.11
, pp. 1698-1722
-
-
Franci, A.1
Drion, G.2
Sepulchre, R.3
-
10
-
-
84878499285
-
A balance equation determines a switch in neuronal excitability
-
A. Franci, G. Drion, V. Seutin, and R. Sepulchre, A balance equation determines a switch in neuronal excitability, PLoS Comput. Biol., 9 (2013), e1003040.
-
(2013)
PLoS Comput. Biol.
, vol.9
, pp. e1003040
-
-
Franci, A.1
Drion, G.2
Seutin, V.3
Sepulchre, R.4
-
11
-
-
2942646686
-
An unfolding theory approach to bursting in fast-slow systems
-
Bristol, UK
-
M. Golubitsky, K. Josic, and T. J. Kaper, An unfolding theory approach to bursting in fast-slow systems, in Global Analysis of Dynamical Systems, Inst. Phys., Bristol, UK, 2001, pp. 277-308.
-
(2001)
Global Analysis of Dynamical Systems, Inst. Phys.
, pp. 277-308
-
-
Golubitsky, M.1
Josic, K.2
Kaper, T.J.3
-
12
-
-
0003270066
-
Singularities and groups in bifurcation theory
-
Springer-Verlag, New York
-
M. Golubitsky and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Appl. Math. Sci. 51, Springer-Verlag, New York, 1985.
-
(1985)
Appl. Math. Sci.
, vol.51
-
-
Golubitsky, M.1
Schaeffer, D.G.2
-
13
-
-
0002016978
-
Asymptotic methods for relaxation oscillations and applications
-
Springer-Verlag, New York
-
J. Grasman, Asymptotic Methods for Relaxation Oscillations and Applications, Appl. Math. Sci. 63, Springer-Verlag, New York, 1987.
-
(1987)
Appl. Math. Sci.
, vol.63
-
-
Grasman, J.1
-
14
-
-
69749095203
-
Robust pacemaking in substantia nigra dopaminergic neurons
-
J. N. Guzman, J. Sánchez-Padilla, C. S. Chan, and D. J. Surmeier, Robust pacemaking in substantia nigra dopaminergic neurons, J. Neurosci., 29 (2009), pp. 11011-11019.
-
(2009)
J. Neurosci.
, vol.29
, pp. 11011-11019
-
-
Guzman, J.N.1
Sánchez-Padilla, J.2
Chan, C.S.3
Surmeier, D.J.4
-
15
-
-
0021768729
-
A model of neuronal bursting using three coupled first-order differential equations
-
J. L. Hindmarsh and R. M. Rose, A model of neuronal bursting using three coupled first-order differential equations, in Proc. Roy. Soc. Lond. B, 221 (1984), pp. 87-102.
-
(1984)
Proc. Roy. Soc. Lond. B
, vol.221
, pp. 87-102
-
-
Hindmarsh, J.L.1
Rose, R.M.2
-
16
-
-
0001441740
-
Invariant manifolds
-
Springer-Verlag, Berlin, Germany
-
M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, Lecture Notes in Math. 583, Springer-Verlag, Berlin, Germany, 1977.
-
(1977)
Lecture Notes in Math.
, vol.583
-
-
Hirsch, M.1
Pugh, C.2
Shub, M.3
-
17
-
-
35649001607
-
A quantitative description of membrane current and its application to conduction and excitation in nerve
-
A. Hodgkin and A. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117 (1952), pp. 500-544.
-
(1952)
J. Physiol.
, vol.117
, pp. 500-544
-
-
Hodgkin, A.1
Huxley, A.2
-
20
-
-
0002316532
-
Geometric singular perturbation theory
-
Springer-Verlag, Berlin
-
C. K. R. Jones, Geometric Singular Perturbation Theory, in Dynamical Systems, Lecture Notes in Math. 1609, Springer-Verlag, Berlin, 1995, pp. 44-120.
-
(1995)
Dynamical Systems, Lecture Notes in Math.
, vol.1609
, pp. 44-120
-
-
Jones, C.K.R.1
-
22
-
-
0036052772
-
Extending geometric singular perturbation theory to nonhyperbolic points-fold and canard points in two dimensions
-
M. Krupa and P. Szmolyan, Extending geometric singular perturbation theory to nonhyperbolic points-fold and canard points in two dimensions, SIAM J. Math. Anal., 33 (2001), pp. 286-314.
-
(2001)
SIAM SIAM J. Math. Anal.
, vol.33
, pp. 286-314
-
-
Krupa, M.1
Szmolyan, P.2
-
23
-
-
0035511458
-
Extending slow manifolds near transcritical and pitchfork singularities
-
M. Krupa and P. Szmolyan, Extending slow manifolds near transcritical and pitchfork singularities, Nonlinearity, 14 (2001), pp. 1473-1491.
-
(2001)
Nonlinearity
, vol.14
, pp. 1473-1491
-
-
Krupa, M.1
Szmolyan, P.2
-
24
-
-
0035839416
-
Relaxation oscillation and canard explosion
-
M. Krupa and P. Szmolyan, Relaxation oscillation and canard explosion, J. Differential Equations, 174 (2001), pp. 312-368.
-
(2001)
J. Differential Equations
, vol.174
, pp. 312-368
-
-
Krupa, M.1
Szmolyan, P.2
-
25
-
-
0032053449
-
A model neuron with activity-dependent conductances regulated by multiple calcium sensors
-
Z. Liu, J. Golowasch, E. Marder, and L. F. Abbott, A model neuron with activity-dependent conductances regulated by multiple calcium sensors, J. Neurosci., 18 (1998), pp. 2309-2320.
-
(1998)
J. Neurosci.
, vol.18
, pp. 2309-2320
-
-
Liu, Z.1
Golowasch, J.2
Marder, E.3
Abbott, L.F.4
-
26
-
-
0003957404
-
Differential equations with small parameters and relaxation oscillations
-
Plenum, New York
-
E. F. Mishchenko and N. K. Rozov, Differential Equations with Small Parameters and Relaxation Oscillations, Math. Concepts Methods Sci. Engrg. 13, Plenum, New York, 1980.
-
(1980)
Math. Concepts Methods Sci. Engrg.
, vol.13
-
-
Mishchenko, E.F.1
Rozov, N.K.2
-
27
-
-
71849099262
-
CaV1.3 channel voltage dependence, not Ca2+ selectivity, drives pacemaker activity and amplifies bursts in nigral dopamine neurons
-
I. Putzier, P.H.M. Kullmann, J.P. Horn, and E.S. Levitan, CaV1.3 channel voltage dependence, not Ca2+ selectivity, drives pacemaker activity and amplifies bursts in nigral dopamine neurons, J. Neurosci., 29 (2009), pp. 15414-15419.
-
(2009)
J. Neurosci.
, vol.29
, pp. 15414-15419
-
-
Putzier, I.1
Kullmann, P.H.M.2
Horn, J.P.3
Levitan, E.S.4
-
28
-
-
0022332422
-
Excitation dynamics: Insights from simplified membrane models
-
J. Rinzel, Excitation dynamics: Insights from simplified membrane models, Fed. Proc., 44 (1985), pp. 2944-2946.
-
(1985)
Fed. Proc.
, vol.44
, pp. 2944-2946
-
-
Rinzel, J.1
-
29
-
-
0000357907
-
A formal classification of bursting mechanisms in excitable systems
-
Springer, New York
-
J. Rinzel, A formal classification of bursting mechanisms in excitable systems, in Mathematical Topics in Population Biology, Morphogenesis and Neurosciences, Springer, New York, 1987, pp. 267-281.
-
(1987)
Mathematical Topics in Population Biology, Morphogenesis and Neurosciences
, pp. 267-281
-
-
Rinzel, J.1
-
30
-
-
0035254572
-
Tonic and burst firing: Dual modes of thalamocortical relay
-
S. M. Sherman, Tonic and burst firing: Dual modes of thalamocortical relay, Trends Neurosci., 24 (2001), pp. 122-126.
-
(2001)
Trends Neurosci.
, vol.24
, pp. 122-126
-
-
Sherman, S.M.1
-
31
-
-
54949130175
-
Methods of the qualitative theory for the Hindmarsh-Rose model: A case study. A tutorial
-
A. Shilnikov and M. Kolomiets, Methods of the qualitative theory for the Hindmarsh-Rose model: A case study. A tutorial, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 18 (2008), pp. 2141-2168.
-
(2008)
Internat. J. Bifur. Chaos Appl. Sci. Engrg.
, vol.18
, pp. 2141-2168
-
-
Shilnikov, A.1
Kolomiets, M.2
-
32
-
-
0347931871
-
Effects of noise on elliptic bursters
-
J. Su, J. Rubin, and D. Terman, Effects of noise on elliptic bursters, Nonlinearity, 17 (2004), pp. 133-157.
-
(2004)
Nonlinearity
, vol.17
, pp. 133-157
-
-
Su, J.1
Rubin, J.2
Terman, D.3
-
33
-
-
0026239399
-
Chaotic spikes arising from a model of bursting in excitable membranes
-
D. Terman, Chaotic spikes arising from a model of bursting in excitable membranes, SIAM J. Appl. Math., 51 (1991), pp. 1418-1450.
-
(1991)
SIAM SIAM J. Appl. Math.
, vol.51
, pp. 1418-1450
-
-
Terman, D.1
-
34
-
-
33645049113
-
Norepinephrine differentially modulates different types of respiratory pacemaker and nonpacemaker neurons
-
J.-C. Viemari and J.-M. Ramirez, Norepinephrine differentially modulates different types of respiratory pacemaker and nonpacemaker neurons, J. Neurophysiol., 95 (2006), pp. 2070-2082.
-
(2006)
J. Neurophysiol.
, vol.95
, pp. 2070-2082
-
-
Viemari, J.-C.1
Ramirez, J.-M.2
-
35
-
-
0033019174
-
Current clamp and modeling studies of lowthreshold calcium spikes in cells of the cat's lateral geniculate nucleus
-
X. J. Zhan, C. L. Cox, J. Rinzel, and S. M. Sherman, Current clamp and modeling studies of lowthreshold calcium spikes in cells of the cat's lateral geniculate nucleus, J. Neurophysiol., 81 (1999), pp. 2360-2373.
-
(1999)
J. Neurophysiol.
, vol.81
, pp. 2360-2373
-
-
Zhan, X.J.1
Cox, C.L.2
Rinzel, J.3
Sherman, S.M.4
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