SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3520-3576, January 2021.
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.

中文翻译：

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特征值的脉冲复制和累积

SIAM 数学分析杂志，第 53 卷，第 3 期，第 3520-3576 页，2021 年 1 月
。受 FitzHugh--Nagumo 方程中观察到的脉冲复制现象的启发，我们研究了慢/快轮廓表现出鸭式转变的行进脉冲。我们表明，关于此类脉冲的 PDE 线性化的频谱可能包含许多点特征值，这些点特征值随着慢尺度参数接近零而累积到曲线的联合上。极限集与鸭式跃迁中涉及的均匀静止状态的绝对谱有关。我们的结果是为允许适当的慢/快结构的一般系统制定的。