Dresden 2011 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 14: Delay Dynamics

DY 14.1: Vortrag

Dienstag, 15. März 2011, 14:00–14:15, ZEU 255

Dimension of linear delay differential equations with time-varying delay — •Andreas Otto and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

It is well known, that delay differential equations (DDE) with constant delay constitute an infinite dimensional dynamical system. On the other hand, the phase space of DDE with time-varying delay can be also finite dimensional.

In this contribution we investigate the dimension of DDE with time-varying delay. Depending on the structure of the deviating argument the the asymptotic dimension of the solution space can be infinite or finite. Furthermore, it is possible that the dimension of the solution space is only an infinite dimensional subspace of the domain of the initial function.

We present a method to calculate the dimension of DDE with time-varying delay. The iterated map of the stepwise retarded access by the deviating argument up to values of the initial function can characterize the dimensional behavior of the solution of DDE with time-varying delay. The results of the presented method are verified by the Lyapunov spectrum of the discretized DDE.