Citation Relationships



Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B Biol Sci 221:87-102 [PubMed]

   A model of neuronal bursting using three coupled first order diff. eqs. (Hindmarsh & Rose 1984)

References and models cited by this paper

References and models that cite this paper

Arrowsmith DK,Place CM (1982) Ordinary differential equations

Colding-Jørgensen M (1976) A description of adaptation in excitable membranes. J Theor Biol 63:61-87 [PubMed]

Connor JA, Stevens CF (1971) Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma. J Physiol 213:31-53 [PubMed]

Dickinson PS, Nagy F (1983) Control of a central pattern generator by an identified modulatory interneurone in crustacea. II. Induction and modification of plateau properties in pyloric neurones. J Exp Biol 105:59-82 [PubMed]

Fitzhugh R (1961) Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophys J 1:445-66 [PubMed]

Game CJ (1982) BVP models of nerve membrane. Nature 299:375 [PubMed]

Gola M (1974) [Bursting pacemaker neurons in molluscs. Slow cyclic variation of ionic conductances (author's transl)]. Pflugers Arch 352:17-36 [PubMed]

Gorman AL, Hermann A (1982) Quantitative differences in the currents of bursting and beating molluscan pace-maker neurones. J Physiol 333:681-99 [PubMed]

Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296:162-4 [PubMed]

HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

   Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
   Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]

Jordan DW,Smith P (1977) Nonlinear ordinary differential equations

Partridge LD, Stevens CF (1976) A mechanism for spike frequency adaptation. J Physiol 256:315-32 [PubMed]

Plant RE, Kim M (1976) Mathematical description of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations. Biophys J 16:227-44 [Journal] [PubMed]

Russell DF, Hartline DK (1982) Slow active potentials and bursting motor patterns in pyloric network of the lobster, Panulirus interruptus. J Neurophysiol 48:914-37 [Journal] [PubMed]

Schwindt P, Crill W (1980) Role of a persistent inward current in motoneuron bursting during spinal seizures. J Neurophysiol 43:1296-318 [Journal] [PubMed]

Smith TG, Barker JL, Gainer H (1975) Requirements for bursting pacemaker potential activity in molluscan neurones. Nature 253:450-2 [PubMed]

Thompson SH, Smith SJ (1976) Depolarizing afterpotentials and burst production in molluscan pacemaker neurons. J Neurophysiol 39:153-61 [Journal] [PubMed]

Wilson WA, Wachtel H (1974) Negative resistance characteristic essential for the maintenance of slow oscillations in bursting neurons. Science 186:932-4 [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. J Neurophysiol 66:2107-24 [Journal] [PubMed]

   Bursting activity of neuron R15 in Aplysia (Canavier et al 1991, Butera et al 1995) [Model]

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]

Heitmann S, Breakspear M (2018) Chapter 1 Handbook for the Brain Dynamics Toolbox: Version 2018a :1-88 [Journal]

   Brain Dynamics Toolbox (Heitmann & Breakspear 2016, 2017, 2018) [Model]

Naze S, Bernard C, Jirsa V (2015) Computational modeling of seizure dynamics using coupled neuronal networks: factors shaping epileptiform activity. PLoS Comput Biol 11:e1004209 [Journal] [PubMed]

   Multiscale modeling of epileptic seizures (Naze et al. 2015) [Model]

Nowotny T, Levi R, Selverston AI (2008) Probing the dynamics of identified neurons with a data-driven modeling approach. PLoS One 3:e2627 [Journal] [PubMed]

   Data-driven, HH-type model of the lateral pyloric (LP) cell in the STG (Nowotny et al. 2008) [Model]

Stewart RD, Bair W (2009) Spiking neural network simulation: numerical integration with the Parker-Sochacki method. J Comput Neurosci 27:115-33 [Journal] [PubMed]

   Numerical Integration of Izhikevich and HH model neurons (Stewart and Bair 2009) [Model]

Stiesberg GR, Reyes MB, Varona P, Pinto RD, Huerta R (2007) Connection topology selection in central pattern generators by maximizing the gain of information. Neural Comput 19:974-93 [Journal] [PubMed]

(25 refs)