Regensburg 2016 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 51: Delay and feedback Dynamics

DY 51.4: Talk

Thursday, March 10, 2016, 10:45–11:00, H47

The Hill-Floquet method for the analysis of periodic solutions in time-delay systems — •Andreas Otto and Günter Radons — Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

The Hill-Floquet method for the calculation of Floquet multipliers for periodic systems is introduced. The stability of an equilibrium can be analyzed via the characteristic equation. According to Floquet theory, the perturbations around a periodic solution can be decomposed into a periodic and an exponential part. The Fourier expansion of the periodic terms leads to an infinite dimensional characteristic equation, which is known as central equation in solid state physics, multi-frequency approach in engineering or Hill’s infinite determinant method.

Based on this method a general transformation from the original finite dimensional periodic system to an infinite dimensional time-invariant system is presented, the so-called Hill-Floquet transformation. The transformation can be also used for the transformation of delay differential equations (DDEs) with periodic coefficients to time-invariant DDEs. As a result, a large variety of established methods for autonomous DDEs are made available for the analysis of periodic DDEs. In this talk, the Hill-Floquet method is combined with a Chebyshev collocation method for the numerical stability analysis of periodic solutions of nonlinear DDEs.