Multiple Bifurcations in a Polynomial Model of Bursting Oscillations |
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Authors: | G de Vries |
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Institution: | (1) Mathematical Research Branch, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, BSA Building, Suite 350, Bethesda, MD 20892, USA e-mail: gerda@helix.nih.gov, US |
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Abstract: | Summary. Bursting oscillations are commonly seen to be the primary mode of electrical behaviour in a variety of nerve and endocrine
cells, and have also been observed in some biochemical and chemical systems. There are many models of bursting. This paper
addresses the issue of being able to predict the type of bursting oscillation that can be produced by a model. A simplified
model capable of exhibiting a wide variety of bursting oscillations is examined. By considering the codimension-2 bifurcations
associated with Hopf, homoclinic, and saddle-node of periodics bifurcations, a bifurcation map in two-dimensional parameter
space is created. Each region on the map is characterized by a qualitatively distinct bifurcation diagram and, hence, represents
one type of bursting oscillation. The map elucidates the relationship between the various types of bursting oscillations.
In addition, the map provides a different and broader view of the current classification scheme of bursting oscillations.
Received October 9, 1996; revised June 16, 1997, and accepted September 26, 1997 |
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Keywords: | , bursting oscillations, classification of bursting oscillations, multiple bifurcation theory, codimension |
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