Fenichel Theory for Multiple Time Scale Singular Perturbation Problems
Fenichel Theory for Multiple Time Scale Singular Perturbation Problems
复制标题
DOI：
10.1137/16m1067202
复制
发表时间：
2017-01-01
影响因子：
2.1
通讯作者：
Teixeira, Marco Antonio
中科院分区：
文献类型：
--
作者：
Cardin, Pedro Toniol;Teixeira, Marco Antonio
本文研究了由RI上的（n - 1）-参数光滑向量场族表示的奇摄动常微分方程组的几何性质，其中n >= 2。这种系统的固有特性是存在任意数量n的时间尺度。对于n - 2，本文提出的几何方法报告给Fenichel的快慢系统理论[N. Fenichel，J.微分方程，31（1979），pp. 53-98]。本文推广了Fenichel [N. Fenichel，J.微分方程，31（1979），pp. 53-98]涉及任何数量的时间尺度的系统。
This paper is concerned with a geometric study of singularly perturbed systems of ordinary differential equations expressed by (n - 1)-parameter families of smooth vector fields on RI, where n >= 2. The inherent characteristic of such systems is the presence of an arbitrary number n of time scales. For n - 2, the proposed geometric approach in this paper reports to Fenichel theory of fast-slow systems [N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98]. We extend the three main theorems due to Fenichel [N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98] to systems involving any number of time scales.