Citation Relationships



Shorten PR, Wall DJ (2000) A Hodgkin-Huxley model exhibiting bursting oscillations. Bull Math Biol 62:695-715 [PubMed]

References and models cited by this paper

References and models that cite this paper

Adler M, Wong BS, Sabol SL, Busis N, Jackson MB, Weight FF (1983) Action potentials and membrane ion channels in clonal anterior pituitary cells. Proc Natl Acad Sci U S A 80:2086-90 [PubMed]

Alberts B, Bray D, Lewis J, Kaff M, Roberts K, Watson JD (1983) Molecular Biology of the Cell (1st Ed)

Arnold V, Iliyashenko Y, Shilinikov L (1994) Dynamical Systems Encyclopaedia of Mathematical Sciences

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

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

Chay TR (1997) Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells. Biophys J 73:1673-88 [Journal] [PubMed]

De_vries G (1998) Multiple bifurcations in a polynomial model of bursting oscillations J Nonlinear Sci 8:281-316

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

Gall D, Susa I (1999) Effect of Na/Ca exchange on plateau fraction and [Ca]i in models for bursting in pancreatic beta-cells. Biophys J 77:45-53 [Journal] [PubMed]

Guérineau N, Corcuff JB, Tabarin A, Mollard P (1991) Spontaneous and corticotropin-releasing factor-induced cytosolic calcium transients in corticotrophs. Endocrinology 129:409-20 [Journal] [PubMed]

Hale J, Kocak H (1991) Dynamics and Bifurcations

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]

Holden L, Erneux T (1993) Slow passage through a Hopf bifurcation: from oscillatory to steady state solutions. Siam J Appl Math 53:1045-1058

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

Kuryshev YA, Childs GV, Ritchie AK (1995) Three high threshold calcium channel subtypes in rat corticotropes. Endocrinology 136:3916-24 [Journal] [PubMed]

Kuryshev YA, Childs GV, Ritchie AK (1996) Corticotropin-releasing hormone stimulates Ca2+ entry through L- and P-type Ca2+ channels in rat corticotropes. Endocrinology 137:2269-77 [Journal] [PubMed]

Kuryshev YA, Haak L, Childs GV, Ritchie AK (1997) Corticotropin releasing hormone inhibits an inwardly rectifying potassium current in rat corticotropes. J Physiol 502 ( Pt 2):265-79 [PubMed]

Kuznetsov Y (1998) Elements of applied bifurcation theory (2nd ed.)

LeBeau AP, Robson AB, McKinnon AE, Donald RA, Sneyd J (1997) Generation of action potentials in a mathematical model of corticotrophs. Biophys J 73:1263-75 [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]

Li YX, Rinzel J, Vergara L, Stojilkovic SS (1995) Spontaneous electrical and calcium oscillations in unstimulated pituitary gonadotrophs. Biophys J 69:785-95 [Journal] [PubMed]

Li YX, Stojilkovic SS, Keizer J, Rinzel J (1997) Sensing and refilling calcium stores in an excitable cell. Biophys J 72:1080-91 [Journal] [PubMed]

Mollard P, Vacher P, Guerin J, Rogawski MA, Dufy B (1987) Electrical properties of cultured human adrenocorticotropin-secreting adenoma cells: effects of high K+, corticotropin-releasing factor, and angiotensin II. Endocrinology 121:395-405 [Journal] [PubMed]

Neher E, Augustine GJ (1992) Calcium gradients and buffers in bovine chromaffin cells. J Physiol 450:273-301 [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

Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences., Teramoto E:Yamaguti M, ed. pp.267

Rinzel J, Lee Y (1986) On different mechanisms for membranepotential bursters Nonlinear Oscillations in Biology and Chemistry, Othmer H, ed.

Rush ME, Rinzel J (1994) Analysis of bursting in a thalamic neuron model. Biol Cybern 71:281-91 [PubMed]

Shorten PR, Lebeau AP, Robson AB, Mckinnon AE, Wall DJN (1999) A role of the endoplasmic reticulum in a mathematical model of corticotrophaction potentials Technical Report 173121

Shorten PR, Robson AB, Mckinnon AE, Wall DJN (1999) The inward rectifier in a model of corticotroph electrical activity Technical Report 185122

Doiron B, Laing C, Longtin A, Maler L (2002) Ghostbursting: a novel neuronal burst mechanism. J Comput Neurosci 12:5-25 [PubMed]

Shorten PR, Robson AB, McKinnon AE, Wall DJ (2000) CRH-induced electrical activity and calcium signalling in pituitary corticotrophs. J Theor Biol 206:395-405 [Journal] [PubMed]

Wang J,Si W, Che Y, Fei X (2008) Spike trains in Hodgkin–Huxley model and of acupuncture manipulations Chaos, Solitons and Fractals 36:890-900 [Journal]

   Spike trains in Hodgkin–Huxley model and ISIs of acupuncture manipulations (Wang et al. 2008) [Model]

(33 refs)