Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations
نویسنده
چکیده
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 (SD-DDEs), 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 statedependent delays. This is an alternative and extension to the original Hopf bifurcation theorem for SD-DDEs by Eichmann (2006).
منابع مشابه
DDE-BIFTOOL v. 3.1.1 Manual — Bifurcation analysis of delay differential equations
5 Delay differential equations 6 5.1 Equations with constant delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.1.1 Steady states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.1.2 Periodic orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.1.3 Connecting orbits . . . . . . . . . . . . . . . . . . . . . . ....
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