Bulletin of Mathematical Biology

, Volume 57, Issue 3, pp 413–439

Topological and phenomenological classification of bursting oscillations

  • Richard Bertram
  • Manish J. Butte
  • Tim Kiemel
  • Arthur Sherman

DOI: 10.1007/BF02460633

Cite this article as:
Bertram, R., Butte, M.J., Kiemel, T. et al. Bltn Mathcal Biology (1995) 57: 413. doi:10.1007/BF02460633


We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (inMathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.

Copyright information

© Society for Mathematical Biology 1995

Authors and Affiliations

  • Richard Bertram
    • 1
  • Manish J. Butte
    • 2
  • Tim Kiemel
    • 3
  • Arthur Sherman
  1. 1.National Institutes of Diabetes and Digestive and Kidney Diseases, Mathematical Research BranchNational Institutes of HealthBethesdaUSA
  2. 2.Brown UniversityProvidenceUSA
  3. 3.Department of ZoologyUniversity of MarylandCollege ParkUSA

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