Multiple bifurcations in a polynomial model of bursting oscillations

被引:45
作者
de Vries, G [1 ]
机构
[1] NIDDKD, Math Res Branch, NIH, Bethesda, MD 20892 USA
基金
加拿大自然科学与工程研究理事会;
关键词
bursting oscillations; classification of bursting oscillations; multiple bifurcation theory; codimension;
D O I
10.1007/s003329900053
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 coated. 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.
引用
收藏
页码:281 / 316
页数:36
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