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Vo T, Bertram R, Tabak J, Wechselberger M (2010) Mixed mode oscillations as a mechanism for pseudo-plateau bursting. J Comput Neurosci 28:443-58 [PubMed]

   Mixed mode oscillations as a mechanism for pseudo-plateau bursting (Vo et al. 2010)

References and models cited by this paper

References and models that cite this paper

Benoit E (1983) Syst'emes lents-rapides dans r3 et leur canards. Asterisque 109-110:159-191
Brons M, Kaper TJ, Rotstein HG (2008) Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis. Chaos 18:015101 [Journal] [PubMed]
Brons M, Krupa M, Wechselberger M (2006) Mixed mode oscillations due to the generalized canard phenomenon Fields Institute Communications 49:39-63
Desroches M, Krauskopf B, Osinga HM (2008) Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system. Chaos 18:015107 [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
Erchova I, McGonigle DJ (2008) Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data. Chaos 18:015115 [Journal] [PubMed]
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, Wechselberger M (2009) Canards, clusters and synchronization in a weakly coupled interneuron model Siam Journal On Applied Dynamical Systems 8:253-278
Fenichel N (1979) Geometric singular perturbation theory for ordinary differential equations J Diff Eqn 31:53-98
Guckenheimer J (2008) Singular Hopf bifurcation in systems with two slow variables Siam Journal On Applied Dynamical Systems 7:1355-1377
Guckenheimer J, Harris-Warrick R, Peck J, Willms A (1997) Bifurcation, bursting, and spike frequency adaptation. J Comput Neurosci 4:257-77 [PubMed]
Jones CKRT (1995) Geometric singular perturbation theory Dynamical Systems Lecture Notes in Math. 1609:44-118
Kinard TA, de Vries G, Sherman A, Satin LS (1999) Modulation of the bursting properties of single mouse pancreatic beta-cells by artificial conductances. Biophys J 76:1423-35 [Journal] [PubMed]
Krupa M, Popovic N, Kopell N, Rotstein HG (2008) Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron. Chaos 18:015106 [Journal] [PubMed]
Krupa M, Wechselberger M (2010) Local analysis near a folded saddle-node singularity Journal of Differential Equations 248(12):2841-2888
Kuryshev YA, Childs GV, Ritchie AK (1996) Corticotropin-releasing hormone stimulates Ca2+ entry through L- and P-type Ca2+ channels in rat corticotropes. Endocrinology 137:2269-77 [Journal] [PubMed]
LeBeau AP, Robson AB, McKinnon AE, Sneyd J (1998) Analysis of a reduced model of corticotroph action potentials. J Theor Biol 192:319-39 [PubMed]
Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193-213 [Journal] [PubMed]
   Morris-Lecar model of the barnacle giant muscle fiber (Morris, Lecar 1981) [Model]
Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences., Teramoto E:Yamaguti M, ed. pp.267
Rinzel J, Ermentrout B (1998) Analysis of neural excitability and oscillations. Methods In Neuronal Modeling 2nd Edition, Segev I, Koch C, ed. pp.251
Rotstein H, Wechselberger M, Kopell N (2008) Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model Siam Journal Of Dynamic Systems 7:1582-1611
Rubin J, Wechselberger M (2007) Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model. Biol Cybern 97:5-32 [Journal] [PubMed]
Shorten PR, Robson AB, McKinnon AE, Wall DJ (2000) CRH-induced electrical activity and calcium signalling in pituitary corticotrophs. J Theor Biol 206:395-405 [Journal] [PubMed]
Stern JV, Osinga HM, LeBeau A, Sherman A (2008) Resetting behavior in a model of bursting in secretory pituitary cells: distinguishing plateaus from pseudo-plateaus. Bull Math Biol 70:68-88 [Journal] [PubMed]
Szmolyan P, Wechselberger M (2001) Canards in 3 J Diff Eqn 177:419-453
Szmolyan P, Wechselberger M (2004) Relaxation oscillations in R3 Journal Of Differential Equations 200:69-104
Tabak J, Toporikova N, Freeman ME, Bertram R (2007) Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents. J Comput Neurosci 22:211-22 [Journal] [PubMed]
   Low dose of dopamine may stimulate prolactin secretion by increasing K currents (Tabak et al. 2006) [Model]
Toporikova N, Tabak J, Freeman ME, Bertram R (2008) A-type K(+) current can act as a trigger for bursting in the absence of a slow variable. Neural Comput 20:436-51 [Journal] [PubMed]
Tsaneva-Atanasova K, Sherman A, van Goor F, Stojilkovic SS (2007) Mechanism of spontaneous and receptor-controlled electrical activity in pituitary somatotrophs: experiments and theory. J Neurophysiol 98:131-44 [Journal] [PubMed]
Van Goor F, Zivadinovic D, Martinez-Fuentes AJ, Stojilkovic SS (2001) Dependence of pituitary hormone secretion on the pattern of spontaneous voltage-gated calcium influx. Cell type-specific action potential secretion coupling. J Biol Chem 276:33840-6 [Journal] [PubMed]
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
Zhang M, Goforth P, Bertram R, Sherman A, Satin L (2003) The Ca2+ dynamics of isolated mouse beta-cells and islets: implications for mathematical models. Biophys J 84:2852-70 [Journal] [PubMed]
Teka W, Tabak J, Bertram R (2012) The relationship between two fast/slow analysis techniques for bursting oscillations. Chaos 22:043117 [Journal] [PubMed]
   The relationship between two fast/slow analysis techniques for bursting oscill. (Teka et al. 2012) [Model]
Vo T, Tabak J, Bertram R, Wechselberger M (2014) A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells. J Comput Neurosci 36:259-78 [Journal] [PubMed]
   Understanding how fast activating K+ channels promote bursting in pituitary cells (Vo et al 2014) [Model]
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