论文标题
入门级功能在与相交特征值的快速慢系统中的功能
Entry-exit functions in fast-slow systems with intersecting eigenvalues
论文作者
论文摘要
我们研究了一类具有两个快速变量和一个慢速的快速系统中稳定性损失的延迟损失，其中快速矢量沿一维临界歧管的线性化具有两个真实的特征值，在累积的收缩和膨胀之前相交，沿任何个体的特征沿着累积的收缩和扩展是平衡的。特征值和特征方向之间的相互作用使已知的入门远期关系的使用不适合计算轨迹退出给定歧管的邻里的点。我们说明了此处考虑的系统类别中可能发生的各种定性场景，我们为入门级别函数提出了新的公式，这些函数是延迟稳定性稳定性现象的现象。
We study delayed loss of stability in a class of fast-slow systems with two fast variables and one slow one, where the linearisation of the fast vector field along a one-dimensional critical manifold has two real eigenvalues which intersect before the accumulated contraction and expansion are balanced along any individual eigendirection. That interplay between eigenvalues and eigendirections renders the use of known entry-exit relations unsuitable for calculating the point at which trajectories exit neighbourhoods of the given manifold. We illustrate the various qualitative scenarios that are possible in the class of systems considered here, and we propose novel formulae for the entry-exit functions that underlie the phenomenon of delayed loss of stability therein.
