Abstract
Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heteroclinic orbit, and that this orbit is monotone. The proof involves a global continuation for heteroclinic orbits.
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Chow, SN., Lin, XB. & Mallet-Paret, J. Transition layers for singularly perturbed delay differential equations with monotone nonlinearities. J Dyn Diff Equat 1, 3–43 (1989). https://doi.org/10.1007/BF01048789
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DOI: https://doi.org/10.1007/BF01048789