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Multiple transition layers in a singularly perturbed differential-delay equation

Published online by Cambridge University Press:  14 November 2011

John Mallet-Paret  and
Roger D. Nussbaum
John Mallet-Paret
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI02912, U.S.A.
Roger D. Nussbaum
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, U.S.A.
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Synopsis

The singularly perturbed differential-delay equation

is studied for a class of step-function nonlinearities f. We show that in general the discrete system

does not mirror the dynamics of (*), even for small ε, but that rather a different system

does. Here F is related to, but different from, f, and describes the evolution of transition layers. In this context, we also study the effects of smoothing out the discontinuities of f.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1119 - 1134
Copyright
Copyright © Royal Society of Edinburgh 1993

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