Abstract
We prove an approximation result for the solutions of a singularly perturbed, nonautonomous ordinary differential equation which has interesting applications to problems in higher dimensions. Here our result is applied to a singularly perturbed, delay differential equation with state dependent time-lags (i.e., aninfinite dimensional problem). We find a new dynamical system (also in infinite dimensions), which describes, in a certain sense, the dynamics of our delay equations for very small values of the singular parameter.
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Paraskevopoulos, P.D. A singular perturbation analysis with applications to delay differential equations. J Dyn Diff Equat 7, 263–285 (1995). https://doi.org/10.1007/BF02219358
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DOI: https://doi.org/10.1007/BF02219358