Multiple impulse solutions to McKean's caricature of the nerve equation. II. Stability

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.