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

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.