Alexander J C, Cai D Y
Department of Mathematics, University of Maryland, College Park 20742.
J Math Biol. 1991;29(5):405-23. doi: 10.1007/BF00160469.
The dynamics of three-variable models of bursting are studied. It is shown that under certain conditions, the dynamics on the attractor can be essentially reduced to two dimensions. The salient dynamics on the attractor can thus be completely described by the return map of a section which is a logistic interval map. Two specific bursting models from the literature are shown to fit in the general framework which is developed. Bifurcation of the full system for one case in investigated and the dynamical behavior on the attractor is shown to depend on the position of a certain nullcline.
研究了爆发的三变量模型的动力学。结果表明，在某些条件下，吸引子上的动力学可基本简化为二维。因此，吸引子上的显著动力学可以完全由一个截面的返回映射来描述，该返回映射是一个逻辑斯谛区间映射。文献中的两个特定爆发模型被证明符合所发展的一般框架。研究了其中一种情况下完整系统的分岔，并表明吸引子上的动力学行为取决于某条零倾线的位置。
