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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 [PubMed]

   Understanding how fast activating K+ channels promote bursting in pituitary cells (Vo et al 2014)

References and models cited by this paper

References and models that cite this paper

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

Berglund N, Gentz B, Kuehn C (2012) Hunting french ducks in a noisy environment Journal Of Differential Equations 252:4786-4841

Bertram R, Butte MJ, Kiemel T, Sherman A (1995) Topological and phenomenological classification of bursting oscillations. Bull Math Biol 57:413-39 [PubMed]

Bertram R, Sherman A (2005) Negative calcium feedback: the road from Chay Keizer Bursting: The Genesis of Rhythm in the Nervous System, Coombes S:Bressloff PC, ed.

Brons M, Kaper TJ, Rotstein HG (2008) Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis Chaos 18:015-101

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

Chiba H (2011) Periodic orbits and chaos in fast-slow systems with bogdanov-takens type fold points Journal Of Differential Equations 250:112-160

del Negro CA, Hsiao CF, Chandler SH (1999) Outward currents influencing bursting dynamics in guinea pig trigeminal motoneurons. J Neurophysiol 81:1478-85 [Journal] [PubMed]

Desroches M, Guckenheimer J, Krauskopf B, Kuehn C, Osinga H, Wechselberger M (2012) Mixed-mode oscillatons with multiple time-scales Siam Rev 54:211-288

Doedel EJ (1981) AUTO: a program for the automatic bifurcation analysis of autonomous systems. Congressus Numerantium 30:265-284

Doedel EJ, Champneys AR, Fairgrieve TF, Kuznetsov YA, Oldeman KE, Paffenroth RC, Sanstede B, (2009) AUTO-07P: continuation and bifurcation software for ordinary differential equations Available from: http:--cmvl.cs

Dorodnitsyn AA (1947) Asymptotic solution of the van der pol equation Proceedings of the Institute of Mechanics of the Academy of Science of the USSR XI

Erchova I, Mcgonigle DJ (2008) Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data Chaos 18:015-115

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]

Ermentrout GB, Wechselberger M (2009) Canards, clusters and synchronization in a weakly coupled interneuron model Siam Journal On Applied Dynamical Systems 8:253-278

Fakler B, Adelman JP (2008) Control of K(Ca) channels by calcium nano/microdomains. Neuron 59:873-81 [Journal] [PubMed]

Fenichel N (1979) Geometric singular perturbation theory for ordinary differential equations J Diff Eqn 31:53-98

Golubitsky M, Kreasimir J, Kaper TJ (2001) An unfolding theory approach to bursting in fast-slow systems Festschrift Dedicated to Floris Takens :277-308

Grasman J (1987) Asymptotic methods for relaxaton oscillations and applications applied Mathematical Sciences

Harvey E, Kirk V, Wechselberger M, Sneyd J (2011) Multiple timescales, mixed mode oscillations and canards in models of intracellular calcium dynamics Journal Of Nonlinear Science 21:639-683

Izhikevich EM (2000) Neural excitability, spiking and bursting Int J Bifurcat Chaos Appl Sci Eng 10:1171-1266

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

   Artificial neuron model (Izhikevich 2003, 2004, 2007) [Model]

Jones CKRT (1995) Geometric singular perturbation theory Dynamical Systems Lecture Notes in Math. 1609:44-118

Kuehn C (2011) A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics Physica D 240:1020-1035

Latorre R, Brauchi S (2006) Large conductance Ca2+-activated K+ (BK) channel: activation by Ca2+ and voltage. Biol Res 39:385-401 [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]

Miranda P, de la Peña P, Gómez-Varela D, Barros F (2003) Role of BK potassium channels shaping action potentials and the associated [Ca(2+)](i) oscillations in GH(3) rat anterior pituitary cells. Neuroendocrinology 77:162-76 [Journal] [PubMed]

Mishchenko EF, Kolesov YUS, Kolesov AYU, Rozov NKH (1994) Asymptotic Methods in Singularly Perturbed Systems

Mishchenko EF, Rozov NK (1980) Differential Equations with Small Parameters and Relaxation Oscillators

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

Nowacki J, Mazlan S, Osinga HM, Tsaneva-atanasova K (2010) The role of large-conductance calcium-activated K+ (BK) channels in shaping bursting oscillations of a somatotroph cell model Physica D 239:485-493

Osinga HM, Tsaneva-Atanasova KT (2010) Dynamics of plateau bursting depending on the location of its equilibrium. J Neuroendocrinol 22:1301-14 [Journal] [PubMed]

Rinzel J (1985) Bursting oscillations in an excitable membrane model, in ordinary and partial differential equations New Lecture Notes in Mathematics 1151:304-316

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, Terman D (2002) Geometric singular perturbation analysis of neuronal dynamics Handbook Of Dynamical Systems, Fiedler B, ed. pp.93

Rubin J, Wechselberger M (2008) The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. Chaos 18:015105 [Journal] [PubMed]

Safiulina VF, Zacchi P, Taglialatela M, Yaari Y, Cherubini E (2008) Low expression of Kv7/M channels facilitates intrinsic and network bursting in the developing rat hippocampus. J Physiol 586:5437-53 [Journal] [PubMed]

Sah P, Faber ES (2002) Channels underlying neuronal calcium-activated potassium currents. Prog Neurobiol 66:345-53 [PubMed]

Sharp AA, O'Neil MB, Abbott LF, Marder E (1993) Dynamic clamp: computer-generated conductances in real neurons. J Neurophysiol 69:992-5 [Journal] [PubMed]

Sherman A, Keizer J, Rinzel J (1990) Domain model for Ca2(+)-inactivation of Ca2+ channels at low channel density. Biophys J 58:985-95 [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]

Stojilkovic SS, Tabak J, Bertram R (2010) Ion channels and signaling in the pituitary gland. Endocr Rev 31:845-915 [Journal] [PubMed]

Stojilkovic SS, Zemkova H, Van Goor F (2005) Biophysical basis of pituitary cell type-specific Ca2+ signaling-secretion coupling. Trends Endocrinol Metab 16:152-9 [Journal] [PubMed]

Szmolyan P, Wechselberger M (2004) Relaxation oscillations in R3 Journal Of Differential Equations 200:69-104

Tabak J, Tomaiuolo M, Gonzalez-Iglesias AE, Milescu LS, Bertram R (2011) Fast-activating voltage- and calcium-dependent potassium (BK) conductance promotes bursting in pituitary cells: a dynamic clamp study. J Neurosci 31:16855-63 [Journal] [PubMed]

Teka W, Tabak J, Vo T, Wechselberger M, Bertram R (2011) The dynamics underlying pseudo-plateau bursting in a pituitary cell model. J Math Neurosci [Journal] [PubMed]

   The dynamics underlying pseudo-plateau bursting in a pituitary cell model (Teka et al. 2011) [Model]

Teka W, Tsaneva-Atanasova K, Bertram R, Tabak J (2011) From plateau to pseudo-plateau bursting: making the transition. Bull Math Biol 73:1292-311 [Journal] [PubMed]

Terman D (1991) Chaotic spikes arising from a model of bursting in excitable membranes. Siam J Appl Math 51:1418-1450

Tsaneva-Atanasova K, Osinga HM, Riess T, Sherman A (2010) Full system bifurcation analysis of endocrine bursting models. J Theor Biol 264:1133-46 [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]

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 [Journal] [PubMed]

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

Vo T, Bertram R, Wechselberger M (2012) Multiple geometric viewpoints of mixed mode dynamics Siam Journal Of Applied Dynamical Systems 12:789-830

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

Wechselberger M, Weckesser W (2009) Bifurcations of mixedmode oscillations in a stellate cell model Physica D 238:1598-1614

Wechselberger W (2012) A propos de canards (apropos canards) Trans Am Math Soc 364:3289-3309

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