Transition layers for singularly perturbed delay differential equations with monotone nonlinearities |
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| Authors: | Shui-Nee Chow Xiao-Biao Lin John Mallet-Paret |
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| Affiliation: | (1) Center for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, 30333 Atlanta, Georgia;(2) Department of Mathematics, North Carolina State University, 27695 Raleigh, North Carolina;(3) Division of Applied Mathematics, Brown University, 02912 Providence, Rhode Island |
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| 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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| Keywords: | Differential delay equations singular perturbations transition layers |
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