Dresden 2006 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 34: Nonlinear Dynamics, Synchronization and Chaos I
DY 34.6: Vortrag
Mittwoch, 29. März 2006, 15:45–16:00, H\"UL 186
Instability of a Limit Cycle in the Van-der-Pol Oscillator with Time Delay — •Kai Schneider1, Viktor Avrutin1, Michael Schanz1, and Axel Pelster2 — 1IPVS, Universität Stuttgart, Universitätsstraße 38, 70569 Stuttgart, Germany — 2Fachbereich Physik, Universität Duisburg-Essen, Universitätsstraße 5, 45117 Essen, Germany
The classical Van-der-Pol oscillator represents a paradigmatic model for electronic circuits with intrinsic negative resistance as, for instance, a tunnel diode. The Van-der-Pol oscillator with time delay represents an extension of this model which takes into account the finite propagation time of signals. We analyze both analytically and numerically the stability of an emerging limit cycle. To this end, we use the Poincaré-Lindstedt method and set up perturbation series for the frequency and the amplitude of the limit cycle. Then we use the Floquet theory for delay differential equations [1] to systematically perform a linear stability analysis for this time periodic reference state. Finally, we compare our analytic results for the instability point of the limit cycle with numerical simulations carried out with the software package AnT 4.669 [2].
[1] C. Simmendinger, A. Pelster, and A. Wunderlin, Phys. Rev. E 59, 5344 (1999)
[2] http://www.AnT4669.de