Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster II

DY 27.3: Poster

Donnerstag, 26. März 2009, 16:00–18:00, P1B

Lyapunov spectrum of linear Delay Differential Equation with time-varying delay — •Andreas Otto and Günter Radons — Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany

Many dynamical systems for instance in engineering science, biology, chemistry, economics and physics are described by Delay Differential Equations (DDE). Hence, there is an essential interest, what happens if delay time changes in time. In this case special phenomena occur in the dynamics of the system.

Our studies on the Lyapunov spectrum of simple linear, scalar, autonomous DDE with periodically time-varying delay try to uncover these special behavior. In spite of inaccuracy in the discrete approximation of the system smaller exponents and their associated Lyapunov vectors contain important information on the dynamics.

Possible extremely small exponents indicate fluctuations of phase space dimension during integration. Furthermore, exponents equal negative infinity stand for a reduced phase space, so that parts of initial function don’t affect solutions of the system. Apart from effect of time-varying delay to the dimension, also different regions of initial function may have differing influence on the solution in contrast to DDE with constant delay.