Bulletin of Mathematical Biology

, Volume 62, Issue 4, pp 695–715 | Cite as

A Hodgkin-Huxley model exhibiting bursting oscillations

  • Paul R. Shorten
  • David J. N. Wall


We investigate bursting behaviour generated in an electrophysiological model of pituitary corticotrophs. The active and silent phases of this mode of bursting are generated by moving between two stable oscillatory solutions. The bursting is indirectly driven by slow modulation of the endoplasmic reticulum Ca2+ concentration. The model exhibits different modes of bursting, and we investigate mode transitions and similar modes of bursting in other Hodgkin-Huxley models. Bifurcation analysis and the use of null-surfaces facilitate a geometric interpretation of the model bursting modes and action potential generation, respectively.


Periodic Orbit Bifurcation Diagram Slow Manifold Unstable Periodic Orbit Stable Periodic Solution 
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Copyright information

© Society for Mathematical Biology 2000

Authors and Affiliations

  • Paul R. Shorten
    • 1
  • David J. N. Wall
    • 1
  1. 1.Biomathematics Research Centre, Department of Mathematics & StatisticsUniversity of CanterburyChristchurch 1New Zealand

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