论文标题
二维ODES中非纤维均衡的稳定指数
Stability Indices of Non-Hyperbolic Equilibria in Two-Dimensional Systems of ODEs
论文作者
论文摘要
我们将二维普通微分方程的系统家族与原点$ 0 $作为非纤维平衡。对于任何数字$ s \ in（ - \ infty， +\ infty）$，我们表明可以在这些方程式中选择一个参数，以便稳定性指数$σ（0）$恰好是$σ（0）= s $。与此相反，对于双曲线平衡$ x $，众所周知，$σ（x）= - \ infty $或$σ（x）=+\ infty $。此外，我们讨论了一个平衡的系统，该系统在局部不稳定但在全球吸引人，突出了本地和非本地稳定性指数之间的一些细微差异。
We consider families of systems of two-dimensional ordinary differential equations with the origin $0$ as a non-hyperbolic equilibrium. For any number $s \in (-\infty, +\infty)$ we show that it is possible to choose a parameter in these equations such that the stability index $σ(0)$ is precisely $σ(0)=s$. In contrast to that, for a hyperbolic equilibrium $x$ it is known that either $σ(x)=-\infty$ or $σ(x)=+\infty$. Furthermore, we discuss a system with an equilibrium that is locally unstable but globally attracting, highlighting some subtle differences between the local and non-local stability indices.
