论文标题
在非标准慢速动力学系统中的接触奇点
Contact singularities in nonstandard slow-fast dynamical systems
论文作者
论文摘要
我们开发了一般表格的奇异扰动（或“慢速”）向量场的触点奇异理论，$ z'= h（z，\ varepsilon）$，$ z \ in \ mathbb {r}^n $和$ \ \ \ varepsilon \ ll 1 $。我们的主要结果是在假设矢量场的前阶项允许合适的分解的假设下，推导了可计算的，与坐标无关的定义方程式的定义方程。可以在各种应用中明确计算此分解。我们通过定位接触褶皱来证明这些可计算标准，并首次在某些非标准模型的生化振荡器中与尖端进行联系。
We develop the contact singularity theory for singularly-perturbed (or `slow-fast') vector fields of the general form $z' = H(z,\varepsilon)$, $z\in\mathbb{R}^n$ and $\varepsilon\ll 1$. Our main result is the derivation of computable, coordinate-independent defining equations for contact singularities under an assumption that the leading-order term of the vector field admits a suitable factorization. This factorization can in turn be computed explicitly in a wide variety of applications. We demonstrate these computable criteria by locating contact folds and, for the first time, contact cusps in some nonstandard models of biochemical oscillators.
