Pulse Replication and Accumulation of Eigenvalues
Pulse Replication and Accumulation of Eigenvalues
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DOI：
10.1137/20m1340113
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
P. Carter;J. Rademacher;Bjorn Sandstede
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文献类型：
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作者：
P. Carter;J. Rademacher;Bjorn Sandstede
出于脉冲复制现象中观察到的FitzHugh-Nagumo方程，我们调查旅行脉冲的慢-快的轮廓表现出鸭式过渡。我们发现，这样的脉冲的PDE线性化的频谱可能包含许多点的特征值，积累到一个联盟的曲线作为慢尺度参数接近零。极限集与鸭式跃迁中所涉及的均匀静止态的绝对谱有关。我们的结果制定一般系统，承认一个适当的慢-快结构。
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.