三维奇异摄动系统平衡点分析的快慢方法  

A Slow-fast Approach for Analyzing Equilibria in Three-dimensional Singularly Perturbed Systems

作　　者：吴宇航 沈建和 WU Yuhang;SHEN Jianhe(College of Mathemaics and Informatics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与信息学院,福建福州350117

出　　处：《福建师范大学学报（自然科学版）》2021年第1期41-48,共8页Journal of Fujian Normal University：Natural Science Edition

基　　金：国家自然科学基金面上项目(11771082)。

摘　　要：通过定义三维空间中的奇异鞍点、奇异稳定(不稳定)结点和奇异鞍结点,并基于隐函数定理和线性化技巧等,证明了具有两个快变量和一个慢变量的三维奇异摄动系统的奇异平衡点在摄动之后保持为该系统的鞍点和结点,最后,将该理论直接应用于Bazykin模型平衡点类型和局部稳定性的的判断.By defining singular saddle,singular stable(unstable)nodes and singular saddle-node in the three-dimensional space,and based on the implicit function theorem as well as linear-ization technique,it is proved that the singular equilibria mentioned above of a three-dimensional singularly perturbed system with two fast and one slow variables remain as the saddles and nodes of the full system after perturbation.Finally,the theory is applied to judge the types and local stability of the equilibria of the Bazykin model.

关 键 词：奇异摄动系统 奇异鞍点 奇异结点 奇异鞍结点 

分 类 号：O174.52[理学—基础数学]