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Multiple impulse solutions to McKean's caricature of the nerve equation. II. Stability
Author(s) -
Wang WeiPing
Publication year - 1988
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160410802
Subject(s) - heaviside step function , superposition principle , impulse (physics) , mathematics , mathematical analysis , amplitude , classical mechanics , physics , quantum mechanics
We study McKean's caricature of a nerve conduction equationwhere H is the Heaviside function. It is proved that an n ‐ple impulse solution resembling the superposition of n unstable solitary impulses has at most 2 n ‐ 1, and at least n , unstable modes: exactly n unstable modes corresponding to the amplitudes and the rest of them corresponding to the spacings. The n amplitude modes always exist. We prove also that for an n ‐ple impulse solution resembling the superposition of n stable solitary impulses, there are at most n ‐ 1 unstable modes and all of them are of spacing type.