7. Geometry of Singular Perturbations: Critical Cases
7. Geometry of Singular Perturbations: Critical Cases
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7.奇异扰动的几何：关键案例
DOI：
10.1137/1.9780898717860.ch7
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发表时间：
2005
影响因子：
5.7
通讯作者：
V. Sobolev
中科院分区：
文献类型：
--
作者：
V. Sobolev
这篇论文是对在违反著名的Tikhonov定理的假设的情况下研究奇摄动系统的几何方法的贡献。7.1引言。奇异摄动系统几何理论的基本原理7.1.1慢积分流形众所周知，自然界各个方面的许多过程都以变量变化率的极大差异为特征，因此奇异摄动常微系统被用作此类过程的模型[21，25，43，44，46，47]。考虑具有向量变量xandy和一个小的正参数ε的常微分系统dx dt=ε)，ε(x，y，t，ε)。
The paper is a contribution to advancing the geometrical approach to the investigation of singularly perturbed systems in cases when the hypotheses of the famous Tikhonov theorem are violated.7.1 Introduction. Elements of the Geometric Theory of Singularly Perturbed Systems7.1.1 Slow integral manifoldsIt is common knowledge that a wide range of processes in various aspects of nature are characterized by extreme differences in the rates of change of variables, so singularly perturbed ordinary differential systems are used as models of such processes [21, 25, 43, 44, 46, 47]).Consider the ordinary differential system dx dt =ƒ (x,y,t,ε), ε dy dt =g (x,y,t,ε), with vector variablesxandy, and a small positive parameter ε.