Adams WB, Levitan IB. (1985). Voltage and ion dependences of the slow currents which mediate bursting in Aplysia neurone R15. The Journal of physiology. 360 [PubMed]
Alonso A, Llinás RR. (1992). Electrophysiology of the mammillary complex in vitro. II. Medial mammillary neurons. Journal of neurophysiology. 68 [PubMed]
Balis UJ, Morris KF, Koleski J, Lindsey BG. (1994). Simulations of a ventrolateral medullary neural network for respiratory rhythmogenesis inferred from spike train cross-correlation. Biological cybernetics. 70 [PubMed]
Benson JA, Levitan IB. (1983). Serotonin increases an anomalously rectifying K+ current in the Aplysia neuron R15. Proceedings of the National Academy of Sciences of the United States of America. 80 [PubMed]
Bertram R, Butte MJ, Kiemel T, Sherman A. (1995). Topological and phenomenological classification of bursting oscillations. Bulletin of mathematical biology. 57 [PubMed]
Bertram R et al. (1995). A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells. Biophysical journal. 68 [PubMed]
Botros SM, Bruce EN. (1990). Neural network implementation of a three-phase model of respiratory rhythm generation. Biological cybernetics. 63 [PubMed]
Brown AM, Schwindt PC, Crill WE. (1994). Different voltage dependence of transient and persistent Na+ currents is compatible with modal-gating hypothesis for sodium channels. Journal of neurophysiology. 71 [PubMed]
Butera RJ, Clark JW, Canavier CC, Baxter DA, Byrne JH. (1995). Analysis of the effects of modulatory agents on a modeled bursting neuron: dynamic interactions between voltage and calcium dependent systems. Journal of computational neuroscience. 2 [PubMed]
Butera RJ, Rinzel J, Smith JC. (1999). Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations Of coupled pacemaker neurons. Journal of neurophysiology. 82 [PubMed]
Byrne JH, Butera RB. (1997). Transient responses of a modeled bursting neuron: Analysis with equilibrium and averaged nullclines Biol Cyber. 77
Calabrese RL, De Schutter E. (1992). Motor-pattern-generating networks in invertebrates: modeling our way toward understanding. Trends in neurosciences. 15 [PubMed]
Canavier CC, Clark JW, Byrne JH. (1991). Simulation of the bursting activity of neuron R15 in Aplysia: role of ionic currents, calcium balance, and modulatory transmitters. Journal of neurophysiology. 66 [PubMed]
Chay TR, Keizer J. (1985). Theory of the effect of extracellular potassium on oscillations in the pancreatic beta-cell. Biophysical journal. 48 [PubMed]
Cohen S, Hindmarsh A. (1996). CVODE, a stiff-nonstiff ODE solver in C. Comput Physics. 10
Del Negro CA, Hsiao CF, Chandler SH, Garfinkel A. (1998). Evidence for a novel bursting mechanism in rodent trigeminal neurons. Biophysical journal. 75 [PubMed]
Demir SS, Butera RJ, DeFranceschi AA, Clark JW, Byrne JH. (1997). Phase sensitivity and entrainment in a modeled bursting neuron. Biophysical journal. 72 [PubMed]
Drummond AH, Benson JA, Levitan IB. (1980). Serotonin-induced hyperpolarization of an indentified Aplysia neuron is mediated by cyclic AMP. Proceedings of the National Academy of Sciences of the United States of America. 77 [PubMed]
Duffin J. (1991). A model of respiratory rhythm generation. Neuroreport. 2 [PubMed]
Epstein IR, Marder E. (1990). Multiple modes of a conditional neural oscillator. Biological cybernetics. 63 [PubMed]
Feldman JL, Smith JC. (1989). Cellular mechanisms underlying modulation of breathing pattern in mammals. Annals of the New York Academy of Sciences. 563 [PubMed]
Fleidervish IA, Friedman A, Gutnick MJ. (1996). Slow inactivation of Na+ current and slow cumulative spike adaptation in mouse and guinea-pig neocortical neurones in slices. The Journal of physiology. 493 ( Pt 1) [PubMed]
Fleidervish IA, Gutnick MJ. (1996). Kinetics of slow inactivation of persistent sodium current in layer V neurons of mouse neocortical slices. Journal of neurophysiology. 76 [PubMed]
Franceschetti S et al. (1995). Ionic mechanisms underlying burst firing in pyramidal neurons: intracellular study in rat sensorimotor cortex. Brain research. 696 [PubMed]
French CR, Sah P, Buckett KJ, Gage PW. (1990). A voltage-dependent persistent sodium current in mammalian hippocampal neurons. The Journal of general physiology. 95 [PubMed]
Funk GD, Smith JC, Feldman JL. (1993). Generation and transmission of respiratory oscillations in medullary slices: role of excitatory amino acids. Journal of neurophysiology. 70 [PubMed]
Gola M. (1974). [Bursting pacemaker neurons in molluscs. Slow cyclic variation of ionic conductances (author's transl)]. Pflugers Archiv : European journal of physiology. 352 [PubMed]
Hoehn K, Watson TW, MacVicar BA. (1993). A novel tetrodotoxin-insensitive, slow sodium current in striatal and hippocampal neurons. Neuron. 10 [PubMed]
Hopkins WF, Satin LS, Cook DL. (1991). Inactivation kinetics and pharmacology distinguish two calcium currents in mouse pancreatic B-cells. The Journal of membrane biology. 119 [PubMed]
Johnson SM, Smith JC, Funk GD, Feldman JL. (1994). Pacemaker behavior of respiratory neurons in medullary slices from neonatal rat. Journal of neurophysiology. 72 [PubMed]
Keizer J, Smolen P. (1991). Bursting electrical activity in pancreatic beta cells caused by Ca(2+)- and voltage-inactivated Ca2+ channels. Proceedings of the National Academy of Sciences of the United States of America. 88 [PubMed]
Koshiya N, Smith JC. (1999). Neuronal pacemaker for breathing visualized in vitro. Nature. 400 [PubMed]
Kramer RH, Zucker RS. (1985). Calcium-dependent inward current in Aplysia bursting pace-maker neurones. The Journal of physiology. 362 [PubMed]
Krinskiĭ VI, Kokoz IuM. (1973). [Analysis of the equations of excitable membranes. I. Reduction of the Hodgkins-Huxley equations to a 2d order system]. Biofizika. 18 [PubMed]
Li YX, Bertram R, Rinzel J. (1996). Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons. Neuroscience. 71 [PubMed]
Li Z, Hatton GI. (1996). Oscillatory bursting of phasically firing rat supraoptic neurones in low-Ca2+ medium: Na+ influx, cytosolic Ca2+ and gap junctions. The Journal of physiology. 496 ( Pt 2) [PubMed]
Llinás RR. (1988). The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science (New York, N.Y.). 242 [PubMed]
Lüthi A, McCormick DA. (1998). H-current: properties of a neuronal and network pacemaker. Neuron. 21 [PubMed]
Marder E, Abbott LF, Hooper SL. (1991). Oscillating networks: control of burst duration by electrically coupled neurons Neural Comput. 3
Mathieu PA, Roberge FA. (1971). Characteristics of pacemaker oscillations in Aplysia neurons. Canadian journal of physiology and pharmacology. 49 [PubMed]
McCormick DA, Huguenard JR. (1992). A model of the electrophysiological properties of thalamocortical relay neurons. Journal of neurophysiology. 68 [PubMed]
Miura RM, Devries G. (1998). Analysis of a class of models of bursting electrical activity in pancreatic b-cells. Siam J Appl Math. 58
Miura RM, Pernarowski M, Kevorkian J. (1992). Perturbation techniques for models of bursting electrical activity in pancreatic b-cells. Siam J Appl Math. 52
Nadim F, Calabrese RL. (1997). A slow outward current activated by FMRFamide in heart interneurons of the medicinal leech. The Journal of neuroscience : the official journal of the Society for Neuroscience. 17 [PubMed]
Ogilvie MD, Gottschalk A, Anders K, Richter DW, Pack AI. (1992). A network model of respiratory rhythmogenesis. The American journal of physiology. 263 [PubMed]
Oka Y. (1996). Characterization of TTX-resistant persistent Na+ current underlying pacemaker potentials of fish gonadotropin-releasing hormone (GnRH) neurons. Journal of neurophysiology. 75 [PubMed]
Onimaru H, Ballanyi K, Richter DW. (1996). Calcium-dependent responses in neurons of the isolated respiratory network of newborn rats. The Journal of physiology. 491 ( Pt 3) [PubMed]
Partridge LD, Swandulla D. (1988). Calcium-activated non-specific cation channels. Trends in neurosciences. 11 [PubMed]
Ramirez JM, Quellmalz UJ, Richter DW. (1996). Postnatal changes in the mammalian respiratory network as revealed by the transverse brainstem slice of mice. The Journal of physiology. 491 ( Pt 3) [PubMed]
Ramirez JM, Richter DW. (1996). The neuronal mechanisms of respiratory rhythm generation. Current opinion in neurobiology. 6 [PubMed]
Rekling JC, Feldman JL. (1998). PreBötzinger complex and pacemaker neurons: hypothesized site and kernel for respiratory rhythm generation. Annual review of physiology. 60 [PubMed]
Richter DW. (1996). Neural regulation of respiration: Rhythmogenesis and afferent control. Comprehensive Human Physiology.. 2
Richter DW, Ballanyi K, Schwarzacher S. (1992). Mechanisms of respiratory rhythm generation. Current opinion in neurobiology. 2 [PubMed]
Richter DW, Gottschalk A, Ogilvie MD, Pack AI. (1994). Computational aspects of the respiratory central pattern generator. Neural Comput. 6
Rinzel J. (1985). Excitation dynamics: insights from simplified membrane models. Federation proceedings. 44 [PubMed]
Rinzel J. (1987). A formal classification of bursting mechanisms in excitable systems. Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences.. 71
Rinzel J, Atwater I. (1986). The b-cell bursting pattern and intracellular calcium. Chapter 22. Ionic Channels in Cells and Model Systems.. 22
Rinzel J, Lee YS. (1987). Dissection of a model for neuronal parabolic bursting. Journal of mathematical biology. 25 [PubMed]
Rinzel J, Smith JC, Butera RJ. (1988). Mechanisms for synchronized bursting of pacemaker neurons in the pre-botzinger complex: computational models and experimental observations. Soc Neurosci Abstr. 24
Rinzel J, Smith JC, Butera RJ. (1997). Rhythm generation and synchronization in a population of bursting neurons with excitatory synaptic coupling: a model for the respiratory oscillator kernel. Soc Neurosci Abstr. 23
Rinzel J, Smith JC, Butera RJ. (1998). Novel frequency control in a population of bursting neurons with excitatory synaptic coupling. Computational Neuroscience: Trends in Research.
Rybak IA, Paton JF, Schwaber JS. (1997). Modeling neural mechanisms for genesis of respiratory rhythm and pattern. II. Network models of the central respiratory pattern generator. Journal of neurophysiology. 77 [PubMed]
Shao XM, Feldman JL. (1997). Respiratory rhythm generation and synaptic inhibition of expiratory neurons in pre-Bötzinger complex: differential roles of glycinergic and GABAergic neural transmission. Journal of neurophysiology. 77 [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]
Sherman A, Rinzel J. (1992). Rhythmogenic effects of weak electrotonic coupling in neuronal models. Proceedings of the National Academy of Sciences of the United States of America. 89 [PubMed]
Smith JC. (1997). Integration of cellular and network mechanisms in mammalian oscillatory motor circuits: Insights from the respiratory oscillator. Neurons, Networks, and Motor Behavior..
Smith JC, Ballanyi K, Richter DW. (1992). Whole-cell patch-clamp recordings from respiratory neurons in neonatal rat brainstem in vitro. Neuroscience letters. 134 [PubMed]
Smith JC, Ellenberger HH, Ballanyi K, Richter DW, Feldman JL. (1991). Pre-Bötzinger complex: a brainstem region that may generate respiratory rhythm in mammals. Science (New York, N.Y.). 254 [PubMed]
Smith JC, Feldman JL, Johnson SM, Funk GD. (1995). Cellular and synaptic mechanisms generating respiratory rhythm: insights from in vitro and computational studies. Ventral Brainstem Mechanisms and Control of Respiration and Blood Pressure..
Smith JC, Koshiya N. (1998). Real-time visualization of respiratory pacemaker neuron activity with calcium-sensitive dyes in the pre-Botziner complex in vitro. Soc Neurosci Abstr. 24
Smolen P, Keizer J. (1992). Slow voltage inactivation of Ca2+ currents and bursting mechanisms for the mouse pancreatic beta-cell. The Journal of membrane biology. 127 [PubMed]
Stafstrom CE, Schwindt PC, Crill WE. (1982). Negative slope conductance due to a persistent subthreshold sodium current in cat neocortical neurons in vitro. Brain research. 236 [PubMed]
Swandulla D, Lux HD. (1985). Activation of a nonspecific cation conductance by intracellular Ca2+ elevation in bursting pacemaker neurons of Helix pomatia. Journal of neurophysiology. 54 [PubMed]
Terman D. (1991). Chaotic spikes arising from a model of bursting in excitable membranes. Siam J Appl Math. 51
Tsien RW, Noble D, Jack JJB. (1983). Linear cable theory Electrical Current Flow in Excitable Cells.
Wilson WA. (1982). Patterned bursting discharge of invertebrate neurons. Cellular Pacemakers.. 7
Athanasiades A, Clark JW, Ghorbel F, Bidani A. (2000). An ionic current model for medullary respiratory neurons. Journal of computational neuroscience. 9 [PubMed]
Ausborn J et al. (2018). Organization of the core respiratory network: Insights from optogenetic and modeling studies. PLoS computational biology. 14 [PubMed]
Ausborn J, Snyder AC, Shevtsova NA, Rybak IA, Rubin JE. (2018). State-dependent rhythmogenesis and frequency control in a half-center locomotor CPG. Journal of neurophysiology. 119 [PubMed]
Breen BJ, Gerken WC, Butera RJ. (2003). Hybrid integrate-and-fire model of a bursting neuron. Neural computation. 15 [PubMed]
Diekman CO, Thomas PJ, Wilson CG. (2017). Eupnea, tachypnea, and autoresuscitation in a closed-loop respiratory control model. Journal of neurophysiology. 118 [PubMed]
Ermentrout GB, Terman DH. (2010). Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics. 35
Ferguson KA, Njap F, Nicola W, Skinner FK, Campbell SA. (2015). Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus. Journal of computational neuroscience. 39 [PubMed]
Fietkiewicz C, Loparo KA, Wilson CG. (2011). Drive latencies in hypoglossal motoneurons indicate developmental change in the brainstem respiratory network. Journal of neural engineering. 8 [PubMed]
Franci A, Drion G, Sepulchre R. (2018). Robust and tunable bursting requires slow positive feedback. Journal of neurophysiology. 119 [PubMed]
Harris KD et al. (2017). Different roles for inhibition in the rhythm-generating respiratory network. Journal of neurophysiology. 118 [PubMed]
Kuo JJ, Lee RH, Zhang L, Heckman CJ. (2006). Essential role of the persistent sodium current in spike initiation during slowly rising inputs in mouse spinal neurones. The Journal of physiology. 574 [PubMed]
Park C, Rubin JE. (2013). Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons. Journal of computational neuroscience. 34 [PubMed]
Purvis LK, Butera RJ. (2005). Ionic current model of a hypoglossal motoneuron. Journal of neurophysiology. 93 [PubMed]
Purvis LK, Smith JC, Koizumi H, Butera RJ. (2007). Intrinsic bursters increase the robustness of rhythm generation in an excitatory network. Journal of neurophysiology. 97 [PubMed]
Rubin JE, Hayes JA, Mendenhall JL, Del Negro CA. (2009). Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations. Proceedings of the National Academy of Sciences of the United States of America. 106 [PubMed]
Rubin JE, Shevtsova NA, Ermentrout GB, Smith JC, Rybak IA. (2009). Multiple rhythmic states in a model of the respiratory central pattern generator. Journal of neurophysiology. 101 [PubMed]
Tabak J, O'Donovan MJ, Rinzel J. (2006). Differential control of active and silent phases in relaxation models of neuronal rhythms. Journal of computational neuroscience. 21 [PubMed]
Teka W, Tabak J, Bertram R. (2012). The relationship between two fast/slow analysis techniques for bursting oscillations. Chaos (Woodbury, N.Y.). 22 [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]
Wilson CG, Fietkiewicz C, Shafer GO, Platt EA. (2016). Variability in respiratory rhythm generation: In vitro and in silico models Communications in Nonlinear Science and Numerical Simulation. 32
Wittman S, Abdala AP, Rubin JE. (2019). Reduced computational modelling of Kölliker-Fuse contributions to breathing patterns in Rett syndrome. The Journal of physiology. 597 [PubMed]
Zylbertal A, Yarom Y, Wagner S. (2017). Synchronous Infra-Slow Bursting in the Mouse Accessory Olfactory Bulb Emerge from Interplay between Intrinsic Neuronal Dynamics and Network Connectivity. The Journal of neuroscience : the official journal of the Society for Neuroscience. 37 [PubMed]
van Drongelen W et al. (2006). Role of persistent sodium current in bursting activity of mouse neocortical networks in vitro. Journal of neurophysiology. 96 [PubMed]