Multiple Impulse Solutions to McKean's Caricature of the Nerve Equation. 2. Stability
Abstract
The Mckean's caricature of a nerve conduction equation del(u )/ delt(t) = del-sq(u)/del(x-sq) - u + H(u-a) + v, 0 < a < 1, del(u)/del(t) b < 0, c > 0, where 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 2n - 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. For an n-ple impulse solution resembling the superposition of n stable solitary impulses it is proved that there are at most n - 1 unstable modes and all of them are of spacing type.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1988
- Accession Number
- ADA203021
Entities
People
- Wei-ping Wang
Organizations
- University of North Carolina at Chapel Hill