论文标题
特征值的脉冲复制和积累
Pulse replication and accumulation of eigenvalues
论文作者
论文摘要
在Fitzhugh-nagumo方程中观察到的脉搏复制现象的动机，我们研究了行进脉冲，其缓慢快速的曲线表现出类似can的过渡。我们表明，围绕此类脉冲的PDE线性化的光谱可能包含许多点特征值，这些特征值会随着慢速尺度参数接近零的曲线结合。限制集与类似Canard样过渡的均匀休息状态的绝对光谱有关。我们的结果是针对接受适当缓慢结构的通用系统制定的。
Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow-fast profiles exhibit canard-like transitions. We show that the spectra of the PDE linearization about such pulses may contain many point eigenvalues that accumulate onto a union of curves as the slow scale parameter approaches zero. The limit sets are related to the absolute spectrum of the homogeneous rest states involved in the canard-like transitions. Our results are formulated for general systems that admit an appropriate slow-fast structure.
