Heteroclinic Connection of Periodic Solutions of Delay Differential Equations |
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Authors: | Melanie Rupflin |
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Affiliation: | 1. Departement Mathematik, ETH Zürich, HG G 32.1, R?mistrasse 101, 8092, Zürich, Switzerland
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Abstract: | For a certain class of delay equations with piecewise constant nonlinearities we prove the existence of a rapidly oscillating stable periodic solution and a rapidly oscillating unstable periodic solution. Introducing an appropriate Poincaré map, the dynamics of the system may essentially be reduced to a two dimensional map, the periodic solutions being represented by a stable and a hyperbolic fixed point. We show that the two dimensional map admits a one dimensional invariant manifold containing the two fixed points. It follows that the delay equations under consideration admit a one parameter family of rapidly oscillating heteroclinic solutions connecting the rapidly oscillating unstable periodic solution with the rapidly oscillating stable periodic solution. |
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Keywords: | Delay differential equations Periodic solutions Heteroclinic connection |
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