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DY: Fachverband Dynamik und Statistische Physik

DY 24: Poster I

DY 24.37: Poster

Wednesday, March 28, 2007, 16:00–18:00, Poster D

Noise- and delay-induced dynamics near a global bifurcation — •Roland Aust, Johanne Hizanidis, and Eckehard Schöll — Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany

A generic model exhibiting a saddle-node bifurcation on a limit cycle is investigated. The model has served as a prototype example of excitability, strongly related to the existing global bifurcation, and coherence resonance, when a stochastic force is added [1]. We extend the system including time-delayed feedback control according to the Pyragas scheme and study it both in the presence and absence of noise. We find that the delay itself is able to create new, interesting dynamics. A delay-induced homoclinic bifurcation governed by a characteristic period scaling-law is reported. Using DDE-BIFTOOL [2] a bifurcation diagram in the K−τ plane is given (K being the strength of the control force and τ the time delay). In addition, multistability, including various bifurcations (e. g. saddle-node bifurcation of limit cycles, period-doubling), is found. Finally, we choose our parameters such that no delay-induced bifurcations occur and switch on Gaussian white noise. We compare our results to those of the uncontrolled system, in particular, the coherence resonance curve and features of the oscillations and the related power spectra.

[1] Hu Gang, T. Ditzinger, C.Z. Ning, and H. Haken, Phys. Rev. Lett. 78, 807 (1993).

[2] K. Engelborghs, T. Luzyanina, and D. Roose, ACM Transactions on Mathematical Software, 28, 1 (2002).