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dc.contributor.authorSieber, J.en_GB
dc.date.accessioned2012-10-03T14:47:30Zen_GB
dc.date.accessioned2013-03-20T12:36:37Z
dc.date.issued2012en_GB
dc.description.abstractIn this paper we prove that periodic boundary-value problems (BVPs) for delay differential equations are locally equivalent to finite-dimensional algebraic systems of equations. We rely only on regularity assumptions that follow those of the review by Hartung et al. (2006). Thus, the equivalence result can be applied to differential equations with state-dependent delays, transferring many results of bifurcation theory for periodic orbits to this class of systems. We demonstrate this by using the equivalence to give an elementary proof of the Hopf bifurcation theorem for differential equations with state-dependent delays. This is an extension of the Hopf bifurcation theorem by Eichmann (2006), along with an alternative proof.
dc.identifier.citationVol. 32 (8), pp. 2607 - 2651en_GB
dc.identifier.doi10.3934/dcds.2012.32.2607
dc.identifier.urihttp://hdl.handle.net/10036/3856en_GB
dc.relation.urlhttp://dx.doi.org/10.3934/dcds.2012.32.2607
dc.subjectFunctional differential equations
dc.subjectstate-dependent delay
dc.subjectperiodic orbits
dc.subjectLyapunov-Schmidt reduction
dc.subjectHopf bifurcation
dc.subjectperiodic boundary-value problems
dc.titleFinding periodic orbits in state-dependent delay differential equations as roots of algebraic equationsen_GB
dc.date.available2012-10-03T14:47:30Zen_GB
dc.date.available2013-03-20T12:36:37Z
dc.identifier.issn1078-0947en_GB
dc.descriptionCopyright © 2012 American Institute of Mathematical Sciences
dc.descriptionThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series A following peer review. The definitive publisher-authenticated version (Vol. 32 (8), pp. 2607 – 2651) is available online at: http://dx.doi.org/10.3934/dcds.2012.32.2607
dc.identifier.eissn1553-5231
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series Aen_GB


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