论文标题
慢速hopf分叉的临界性的内在确定
Intrinsic determination of the criticality of a slow-fast Hopf bifurcation
论文作者
论文摘要
在平面中慢速系统中的慢速hopf（或奇异跳跃）点的存在通常是从矢量场的形状中推导的。但是，将系统以正常形式放置可能很麻烦。在专着的“从出生到过渡的堤防”中，启动了缓慢速度矢量场的内在表现，显示动手公式以检查是否存在这种奇异的接触点。我们从单个公式可以检查HOPF分叉的关键性的意义上，从而概括了结果。我们在以非标准形式给出的慢速系统上演示了结果，其中慢速变量并未彼此分开。该公式很方便，因为它不需要临界曲线的任何参数化。
The presence of slow-fast Hopf (or singular Hopf) points in slow-fast systems in the plane is often deduced from the shape of a vector field brought into normal form. It can however be quite cumbersome to put a system in normal form. In the monograph "Canards from birth to transition", an intrinsic presentation of slow-fast vector fields is initiated, showing hands-on formulas to check for the presence of such singular contact points. We generalize the results in the sense that the criticality of the Hopf bifurcation can be checked with a single formula. We demonstrate the result on a slow-fast system given in non-standard form where slow and fast variables are not separated from each other. The formula is convenient since it does not require any parameterization of the critical curve.
