Bertram R, Sherman A. (2005). Negative calcium feedback: the road from Chay Keizer Bursting: The Genesis of Rhythm in the Nervous System.
Brons M, Kaper TJ, Rotstein HG. (2008). Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis. Chaos (Woodbury, N.Y.). 18 [PubMed]
Butera RJ, Rinzel J, Smith JC. (1999). Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. Journal of neurophysiology. 82 [PubMed]
Desroches M, Krauskopf B, Osinga HM. (2008). Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system. Chaos (Woodbury, N.Y.). 18 [PubMed]
Erchova I, McGonigle DJ. (2008). Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data. Chaos (Woodbury, N.Y.). 18 [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
Falke LC, Gillis KD, Pressel DM, Misler S. (1989). 'Perforated patch recording' allows long-term monitoring of metabolite-induced electrical activity and voltage-dependent Ca2+ currents in pancreatic islet B cells. FEBS letters. 251 [PubMed]
Fenichel N. (1979). Geometric singular perturbation theory for ordinary differential equations J Diff Eqn. 31
Guckenheimer J. (2008). Singular Hopf bifurcation in systems with two slow variables Siam Journal On Applied Dynamical Systems. 7
Guckenheimer J, Gueron S, Harris-Warrick RM. (1993). Mapping the dynamics of a bursting neuron. Philosophical transactions of the Royal Society of London. Series B, Biological sciences. 341 [PubMed]
Guckenheimer J, Haiduc R. (2005). Canards at folded nodes Mosc Math J. 5
Guckenheimer J, Harris-Warrick R, Peck J, Willms A. (1997). Bifurcation, bursting, and spike frequency adaptation. Journal of computational neuroscience. 4 [PubMed]
Guckenheimer J et al. (2012). Mixed-mode oscillatons with multiple time-scales Siam Rev. 54
Kinard TA, de Vries G, Sherman A, Satin LS. (1999). Modulation of the bursting properties of single mouse pancreatic beta-cells by artificial conductances. Biophysical journal. 76 [PubMed]
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
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 [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]
Lisman JE. (1997). Bursts as a unit of neural information: making unreliable synapses reliable. Trends in neurosciences. 20 [PubMed]
Osinga HM, Krauskopf B, Desroches M. (2008). The geometry of slow manifolds near a folded node Siam J Appl Dyn Syst. 7
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, Ermentrout B. (1998). Analysis of neural excitability and oscillations. Methods In Neuronal Modeling 2nd Edition.
Rinzel JA. (1987). A formal classification of bursting mechanisms in excitable systems Proc Intl Congress Mathematicians.
Rubin J, Wechselberger M. (2007). Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model. Biological cybernetics. 97 [PubMed]
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]
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, 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. (2001). Canards in 3 J Diff Eqn. 177
Szmolyan P, Wechselberger M. (2004). Relaxation oscillations in R3 Journal Of Differential Equations. 200
Tabak J, Toporikova N, Freeman ME, Bertram R. (2007). Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents. Journal of computational neuroscience. 22 [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]
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, Li YX, Stojilkovic SS. (2001). Paradoxical role of large-conductance calcium-activated K+ (BK) channels in controlling action potential-driven Ca2+ entry in anterior pituitary cells. The Journal of neuroscience : the official journal of the Society for Neuroscience. 21 [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, Krupa M. (2010). Local analysis near a folded saddle-node singularity Journal of Differential Equations. 248(12)
Wechselberger W. (2012). A propos de canards (apropos canards) Trans Am Math Soc. 364
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. Biophysical journal. 84 [PubMed]
del Negro CA, Hsiao CF, Chandler SH. (1999). Outward currents influencing bursting dynamics in guinea pig trigeminal motoneurons. Journal of neurophysiology. 81 [PubMed]
Mondal A, Upadhyay RK. (2018). Diverse neuronal responses of a fractional-order Izhikevich model: journey from chattering to fast spiking Nonlinear Dynamics. 91
Santamaria F, Teka W, Stockton D. (2016). Power-law dynamics of membrane conductances increase spiking diversity in a Hodgkin-Huxley model PLoS Comput Biol. 12(3)
Teka W, Tabak J, Bertram R. (2012). The relationship between two fast/slow analysis techniques for bursting oscillations. Chaos (Woodbury, N.Y.). 22 [PubMed]
Vo T, Tabak J, Bertram R, Wechselberger M. (2014). A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells. Journal of computational neuroscience. 36 [PubMed]