Berglund N, Gentz B, Kuehn C. (2012). Hunting french ducks in a noisy environment Journal Of Differential Equations. 252
Bertram R, Butte MJ, Kiemel T, Sherman A. (1995). Topological and phenomenological classification of bursting oscillations. Bulletin of mathematical biology. 57 [PubMed]
Bertram R, Sherman A. (2005). Negative calcium feedback: the road from Chay Keizer Bursting: The Genesis of Rhythm in the Nervous System.
Bertram R, Wechselberger M, Vo T. (2012). Multiple geometric viewpoints of mixed mode dynamics Siam Journal Of Applied Dynamical Systems. 12
Chiba H. (2011). Periodic orbits and chaos in fast-slow systems with bogdanov-takens type fold points Journal Of Differential Equations. 250
Doedel EJ. (1981). AUTO: a program for the automatic bifurcation analysis of autonomous systems. Congressus Numerantium. 30
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
Ermentrout GB, Terman DH. (2010). Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics. 35
Ermentrout GB, Wechselberger M. (2009). Canards, clusters and synchronization in a weakly coupled interneuron model Siam Journal On Applied Dynamical Systems. 8
Fakler B, Adelman JP. (2008). Control of K(Ca) channels by calcium nano/microdomains. Neuron. 59 [PubMed]
Fenichel N. (1979). Geometric singular perturbation theory for ordinary differential equations J Diff Eqn. 31
Grasman J. (1987). Asymptotic methods for relaxaton oscillations and applications applied Mathematical Sciences. 63
Guckenheimer J et al. (2012). Mixed-mode oscillatons with multiple time-scales Siam Rev. 54
Izhikevich EM. (2000). Neural excitability, spiking and bursting Int J Bifurcat Chaos Appl Sci Eng. 10
Izhikevich EM. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting.
Jones CKRT. (1995). Geometric singular perturbation theory Dynamical Systems Lecture Notes in Math.. 1609
Kaper TJ, Golubitsky M, Kreasimir J. (2001). An unfolding theory approach to bursting in fast-slow systems Festschrift Dedicated to Floris Takens.
Kaper TJ, Rotstein HG, Brons M. (2008). Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis Chaos. 18
Kopell N, Wechselberger M, Rotstein H. (2008). Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model Siam Journal Of Dynamic Systems. 7
Kuehn C. (2011). A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics Physica D. 240
Latorre R, Brauchi S. (2006). Large conductance Ca2+-activated K+ (BK) channel: activation by Ca2+ and voltage. Biological research. 39 [PubMed]
LeBeau AP, Robson AB, McKinnon AE, Sneyd J. (1998). Analysis of a reduced model of corticotroph action potentials. Journal of theoretical biology. 192 [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 [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
Neishtadt AI. (1988). Persistence of stability loss for dynamical bifurcations II Diff Eqn. 24
Osinga HM, Tsaneva-Atanasova KT. (2010). Dynamics of plateau bursting depending on the location of its equilibrium. Journal of neuroendocrinology. 22 [PubMed]
Osinga HM, Tsaneva-atanasova K, Nowacki J, Mazlan S. (2010). The role of large-conductance calcium-activated K+ (BK) channels in shaping bursting oscillations of a somatotroph cell model Physica D. 239
Rinzel J. (1985). Bursting oscillations in an excitable membrane model, in ordinary and partial differential equations New Lecture Notes in Mathematics. 1151
Rinzel J, Baer SM, Erneux T. (1989). The slow passage through Hopf bifurcation: delay, memory ecects, and resonance. J Appl Math. 49
Rubin J, Wechselberger M. (2008). The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. Chaos (Woodbury, N.Y.). 18 [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. The Journal of physiology. 586 [PubMed]
Sah P, Faber ES. (2002). Channels underlying neuronal calcium-activated potassium currents. Progress in neurobiology. 66 [PubMed]
Sharp AA, O'Neil MB, Abbott LF, Marder E. (1993). Dynamic clamp: computer-generated conductances in real neurons. Journal of neurophysiology. 69 [PubMed]
Sherman A, Keizer J, Rinzel J. (1990). Domain model for Ca2(+)-inactivation of Ca2+ channels at low channel density. Biophysical journal. 58 [PubMed]
Sneyd J, Wechselberger M, Kirk V, Harvey E. (2011). Multiple timescales, mixed mode oscillations and canards in models of intracellular calcium dynamics Journal Of Nonlinear Science. 21
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. Bulletin of mathematical biology. 70 [PubMed]
Stojilkovic SS, Tabak J, Bertram R. (2010). Ion channels and signaling in the pituitary gland. Endocrine reviews. 31 [PubMed]
Stojilkovic SS, Zemkova H, Van Goor F. (2005). Biophysical basis of pituitary cell type-specific Ca2+ signaling-secretion coupling. Trends in endocrinology and metabolism: TEM. 16 [PubMed]
Szmolyan P, Wechselberger M. (2004). Relaxation oscillations in R3 Journal Of Differential Equations. 200
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. The Journal of neuroscience : the official journal of the Society for Neuroscience. 31 [PubMed]
Teka W, Tabak J, Vo T, Wechselberger M, Bertram R. (2011). The dynamics underlying pseudo-plateau bursting in a pituitary cell model. Journal of mathematical neuroscience. 1 [PubMed]
Teka W, Tsaneva-Atanasova K, Bertram R, Tabak J. (2011). From plateau to pseudo-plateau bursting: making the transition. Bulletin of mathematical biology. 73 [PubMed]
Terman D. (1991). Chaotic spikes arising from a model of bursting in excitable membranes. Siam J Appl Math. 51
Terman D, Rubin J. (2002). Geometric singular perturbation analysis of neuronal dynamics Handbook Of Dynamical Systems. 2
Tsaneva-Atanasova K, Osinga HM, Riess T, Sherman A. (2010). Full system bifurcation analysis of endocrine bursting models. Journal of theoretical biology. 264 [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. Journal of neurophysiology. 98 [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. The Journal of biological chemistry. 276 [PubMed]
Vo T, Bertram R, Tabak J, Wechselberger M. (2010). Mixed mode oscillations as a mechanism for pseudo-plateau bursting. Journal of computational neuroscience. 28 [PubMed]
Wang XJ et al. (2009). AUTO-07P: continuation and bifurcation software for ordinary differential equations Available from: http:--cmvl.cs.
Wechselberger M. (2005). Existence and bifurcation of canards in 3 in the case of a folded node SIAM J Appl Dynam Sys. 4
Wechselberger M, Brons M, Krupa M. (2006). Mixed mode oscillations due to the generalized canard phenomenon Fields Institute Communications. 49
Wechselberger M, Weckesser W. (2009). Bifurcations of mixedmode oscillations in a stellate cell model Physica D. 238
Wechselberger W. (2012). A propos de canards (apropos canards) Trans Am Math Soc. 364
del Negro CA, Hsiao CF, Chandler SH. (1999). Outward currents influencing bursting dynamics in guinea pig trigeminal motoneurons. Journal of neurophysiology. 81 [PubMed]
Fazli M, Bertram R. (2022). Network Properties of Electrically Coupled Bursting Pituitary Cells Frontiers in endocrinology. 13 [PubMed]