Multiple Oscillatory States and Chaos in the Endogenous Activity of Excitable Cells: Pancreatic β-Cell as an Example

  • Teresa Ree Chay
  • Hong Seok Kang
Part of the NATO ASI Series book series (NSSA, volume 138)


The behaviour of pancreatic β-cells may be described by a system of three nonlinear differential equations that shows multiple oscillatory and chaotic solutions. Bifurcation diagrams of this system are constructed using AUTO.


Hopf Bifurcation Bifurcation Diagram Stable Steady State Hopf Bifurcation Point Unstable Steady State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    P.M. Dean and E.J. Matthews, J. Physiol. 210: 255–264 (1970).PubMedGoogle Scholar
  2. [2]
    H.P. Meissner, J. Physiol. Paris 72: 757–767 (1976).PubMedGoogle Scholar
  3. [3]
    P.M. Beigelman, B. Ribalet and I. Atwater, J. Physiol. Paris 73: 201–217 (1977).PubMedGoogle Scholar
  4. [4]
    B. Ribalet and P.M. Beigelman, Am. J. Physiol. 237: C137 - C146 (1979).PubMedGoogle Scholar
  5. [5]
    I. Atwater, C.M. Dawson, A. Scott, G. Eddlestone and E. Rojas, in “Biochemistry Biophysics of the Pancreatic (3-cell”, ed. Georg Thieme, Verlag, New York, 100–107 (1980).Google Scholar
  6. [6]
    D.L. Cook, Fed. Proc. 43: 2368–2372 (1984).PubMedGoogle Scholar
  7. [7]
    P. Rorsman, H. Abrahamsson, E. Gylfe and B. Hellman, Fed. Eur. Biochem. Soc. Lett. 170: 196–200 (1984).CrossRefGoogle Scholar
  8. [8]
    C.B. Wollheim and T. Pozzan, J. Biol. Chem. 259: 2262–2267 (1986).Google Scholar
  9. [9]
    C.S. Pace, J.T. Tarvin and J.S. Simith, Am. J. Physiol. 244: E3- E18 (1983).Google Scholar
  10. [10]
    G.T. Eddlestone and P.M. Beigelman, Am. J. Physiol. 244: C188 - C197 (1983).PubMedGoogle Scholar
  11. [11]
    D.L. Cook and N. Hales, Nature 311: 271–273 (1984).PubMedCrossRefGoogle Scholar
  12. [12]
    P. Rorsman and G. Trube, J. Physiol. 374: 531–550 (1986).PubMedGoogle Scholar
  13. [13]
    R. Eckert and J.E. Chad, Prog. Biophys. Molec. Biol. 44: 215–267 (1984).CrossRefGoogle Scholar
  14. [14.]
    P. Lebrun, I. Atwater, L.M. Rosario, A. Herchuelz and W.J. Malaisse, Metabolism34: 1122–1127 (1985).PubMedCrossRefGoogle Scholar
  15. [15]
    T.R. Chay, Biol. Cybern. 50: 301–311 (1984).PubMedCrossRefGoogle Scholar
  16. [16]
    T.R. Chay, Physica D 16: 233–242 (1985).CrossRefGoogle Scholar
  17. [17]
    T.R. Chay and J. Rinzel, Biophys. J. 47: 357–366 (1985).PubMedCrossRefGoogle Scholar
  18. [18]
    T.R. Chay, in “Biomathetics, Non Linear Oscillations in Biology and Chemistry”, Lecture Notes in Biomathematics, Springer Verlag, NY (1986).Google Scholar
  19. [19]
    T.R. Chay and Y.S. Lee, Biophys. J. 45: 841–849 (1984).PubMedCrossRefGoogle Scholar
  20. [20]
    T.R. Chay and Y.S. Lee, Biophys. J. 47: 641–651 (1985).PubMedCrossRefGoogle Scholar
  21. [21]
    A. Hodgkin and A.F. Huxley, J. Physiol. (London) 117: 500–544 (1952).Google Scholar
  22. [22]
    A.C. Hindmarsh, “Ordinary Differential Equations Systems Solver”, Lawrence Livermore Laboratory, Livermore, CA, Report (1974).Google Scholar
  23. [23]
    E.J. Doedel, “AUT086 User Manual, Software for continuation and bifurcation problems in ordinary diferential equations”, second printing, California Institute of Technology, February (1986).Google Scholar
  24. [24]
    J.C. Henquin, H.P. Meissner and W. Schmeer, Pflügers Arch. 393: 322–327 (1982).PubMedCrossRefGoogle Scholar
  25. [25]
    P. Lebrun and I. Atwater, Biophys. J. 48: 529–531 (1985)PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Teresa Ree Chay
    • 1
  • Hong Seok Kang
    • 1
  1. 1.Department of Biological SciencesUniversity of PittsburghPittsburghUSA

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