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Heteroclinic connection of periodic solutions of delay differential equations
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Rupflin, Melanie (2009) Heteroclinic connection of periodic solutions of delay differential equations. Journal of Dynamics and Differential Equations, Vol.21 (No.1). pp. 45-71. doi:10.1007/s10884-008-9123-4 ISSN 1040-7294.
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Official URL: http://dx.doi.org/10.1007/s10884-008-9123-4
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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Dynamics and Differential Equations | ||||
Publisher: | Springer | ||||
ISSN: | 1040-7294 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.21 | ||||
Number: | No.1 | ||||
Page Range: | pp. 45-71 | ||||
DOI: | 10.1007/s10884-008-9123-4 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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