Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 30: Spiral Formation and Feedback
DY 30.2: Vortrag
Montag, 7. März 2005, 10:30–10:45, TU H3010
Analytical tools for solving dynamics with time delay — •Andreas Amann1, Wolfram Just2 und Eckehard Schöll1 — 1Institut für Theoretische Physik, Technische Universität Berlin,Hardenbergstr. 36, D–10623 Berlin — 2School of Mathematical Sciences, Queen Mary / University of London, Mile End Road, London E1 4NS, United Kingdom
Time-delay dynamics plays a prominent role in such diverse fields of science as e.g. biological systems, internet traffic, or the control of complex motion. Even for simple model systems analytical approaches face considerable challenges because of infinite dimensional phase spaces. We review in elementary terms how eigenmode expansions can be used to solve linear differential-difference equations and how the spectrum of the corresponding eigenvalue problem can be computed in terms of transcendental functions. We use such schemes for two particular applications: (i) the determination of power spectra of stochastic delay-dynamics, and (ii) the weakly nonlinear perturbation theory for time-delayed feedback control of chaos.