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Existence and uniqueness of travelling waves for a neural network

Published online by Cambridge University Press:  14 November 2011

G. Bard Ermentrout  and
J. Bryce McLeod
G. Bard Ermentrout
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh PA 15260, U.S.A
J. Bryce McLeod
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh PA 15260, U.S.A
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Synopsis

A one-dimensional scalar neural network with two stable steady states is analysed. It is shown that there exists a unique monotone travelling wave front which joins the two stable states. Some additional properties of the wave such as the direction of its velocity are discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 3 , 1993 , pp. 461 - 478
Copyright
Copyright © Royal Society of Edinburgh 1993

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