Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atwater, I., and P. M. Beigelman. 1976. Dynamic characteristics of electrical activity in pancreatic β-cells. Effects of calcium and magnesium. J. Physiol. (Paris) 72:769–786.
Atwater, I., C. M. Dawson, A. Scott, G. Eddlestone, and E. Rojas. 1980. The nature of the oscillatory behavior in electrical activity for pancreatic β-cell. In: Biochemistry Biophysics of Pancreatic-β-Cell, Georg Thieme Verlag, New York. pp. 100–107.
Beigelman, P. M., B. Ribalet, and I. Atwater. 1977. Electrical activity of mouse pancreatic beta-cells II. Effects of glucose and arginine. J. Physiol. (Paris) 73:201–217.
Chay, T. R., and J. Keizer. 1983. Minimal model for membrane oscillations in the pancreatic β-cell. Biophys. J. 42:181–190.
Chay, T. R., and J. Rinzel. Bursting, beating, and chaos in an excitable membrane model. Biophys. J. in press.
Cook, D. L., W. E. Crill, and D. Porte. 1980. Plateau potentials in pancreatic islet cells are voltage-dependent action potentials. Nature 286:404–406.
Doedel, E. J. 1981. AUTO; A program for automatic bifurcation analysis of autonomous systems, (Proc. 10th Manitoba Conf. on Num. Math. and Comput., Winnipeg, Canada), Cong. Num. 30:265–284.
Eddlestone, G. T., A. Goncalves, J. A. Bangham, and E. Rojas. 1984. Electrical coupling between cells in islets of Langerhans from mouse. J. Membrane Biol. 77:1–14.
FitzHugh, R. 1961. Impulses and physiological states in models of nerve membrane. Biophys. J. 1:445–466.
Hindmarsh, J. L., and R. M. Rose. 1984. A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B 221:87–102.
Hodgkin, A. L., and A. F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond) 117:500–544.
Kopell, N., and L. N. Howard. 1975. Bifurcations and trajectories joining critical points. Adv. in Math. 18:306–358.
Meissner, H. P. 1976. Electrical characteristics of the beta-cells in pancreatic creatic islets. J. Physiol. (Paris) 72:757–767.
Plant, R. E. 1978. The effects of calcium++ on bursting neurons. Biophys. J. 21:217–237.
Rinzel, J. Excitation dynamics: insights from simplified membrane models. (pre-print).
Rinzel, J., and W. C. Troy. 1982. Bursting phenomena in a simplified Oregonator flow system model. J. Chem. Phys. 76:1775–1789.
Rinzel, J., and W. C. Troy. 1983. A one-variable map analysis of bursting in the Belousov-Zhabotinskii reaction. In: Oscillations in Mathematical Biology (ed., J. P. E. Hodgson), Lect. Notes in Biomath. 51, Springer, pp. 1–23.
Scott, A. M., I. Atwater, and E. Rojas. 1981. A method for the simultaneous measurement of insulin release and β-cell membrane potential in single mouse islet of Langerhans. Diabetologia 21:470–475.
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Rinzel, J. (1985). Bursting oscillations in an excitable membrane model. In: Sleeman, B.D., Jarvis, R.J. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 1151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074739
Download citation
DOI: https://doi.org/10.1007/BFb0074739
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15694-9
Online ISBN: 978-3-540-39640-6
eBook Packages: Springer Book Archive