Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations
Discrete and Continuous Dynamical Systems - Series A
In 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.
Copyright © 2012 American Institute of Mathematical Sciences
This 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
Vol. 32 (8), pp. 2607 - 2651