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Topological and phenomenological classification of bursting oscillations

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Abstract

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.

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Authors and Affiliations

  1. National Institutes of Diabetes and Digestive and Kidney Diseases, Mathematical Research Branch, National Institutes of Health, BSA Building, Suite 350, 20814, Bethesda, MD, USA

    Richard Bertram

  2. Brown University, Box G-8090, 02912, Providence, RI, USA

    Manish J. Butte

  3. Department of Zoology, University of Maryland, 20742, College Park, MD, USA

    Tim Kiemel

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  1. Richard Bertram
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  2. Manish J. Butte
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  3. Tim Kiemel
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  4. Arthur Sherman
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Bertram, R., Butte, M.J., Kiemel, T. et al. Topological and phenomenological classification of bursting oscillations. Bltn Mathcal Biology 57, 413–439 (1995). https://doi.org/10.1007/BF02460633

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  • DOI: https://doi.org/10.1007/BF02460633

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